fix- gx x +0 ff x 0 and fgx- gfxl 2x" 0 if x 0 so that f and g are compatible on R with the usual metric.
|
|
- Ella Lang
- 5 years ago
- Views:
Transcription
1 Internat. J. Math. & Math. Sci. VOL. Ii NO. 2 (1988) COMPATIBLE MAPPINGS AND COMMON FIXED POINTS (2) GERALD JUNGCK Department of Mathematics Bradley University Peoria, Illinois (Received November 17, 1986) ABSTRACT. A common fixed point theorem of S.L. S.P. Singh is generalized by weakening commutativity hypotheses by increasing the number of functions involved. KEY WORDS AND PHRASES. Common fixed points, commuting mappings, compatible mappings MATHEMATICS SUBJECT CLASSIFICATION CODE. 54H25 I. NTRODUCT ON. In 11] the concept of compatible mappings was introduced as a generalization of commuting maps (fg=gf) The utility of compatibility in the context of fixed point theory was demonstrated by extending a theorem of Park Bae [2] The purpose of this note is to further emulate the compatible map concept. We extend the following strong result of S.L. Singh S.P. Singh 3] by employing compatible maps in lieu of commuting maps, by using four functions as opposed to three. THEOREM. I.I. Let P,Q, T be self maps of a complete metric space (X,d) such that PT=TP, QT=TQ, P(X)LJQ(X)CT(X) If T is continuous there exists r(o,l) such that d(px,qy) < r max {d(tx,ty),d(px,tx), d(qy,ty), 1/2(d(Px,Ty) + d(qy,tx))} for all x,y in X (l.l) Then P, Q, T have a unique common fixed point. 2. PRELIMINARIES. The following definition was given in i] Definition 2.1. Self maps f g of a metric space (X,d) are compatible iff limnd(fgxn,gfxn) 0 whenever {x n is a sequence in X such that lim fx lim t for n some t in n ngxn X Thus, if d(fgx,gfx) +0 as d(fx,gx) -0 f g are compatible. For example, suppose that fx x 2 gx 2x for x in R the set of reals, f g are not commutative, but fix- gx x +0 ff x 0 fgx- gfxl 2x" 0 if x 0 so that f g are compatible on R with the usual metric.
2 286 G. JUNGCK Now maps which commute are clearly compatible, but the converse is false. In fact, compatible maps need not be weakly commutative. Sessa [4 defined self maps f g of a metric space (X,d) to be a weakly commuting pair iff d(gfx,fgx) d(fx,gx) for x in X If f g are weakly commutative they are obviously compatible, but the converse is false as the above example shows (e.g., let x=l.). See 1] for other examples of compatible pairs which are not weakly commutative hence not commuting pairs. 3. MAIN RESULTS. LEMMA 3.1 Let A,B,S, T be self maps of a metric space (X,d) such that A(X)cT(X) B(X)cS(X) let x X If r (0,I) such o that d(ax:by) r max(mxy) for xy cx where Mxy d(ax,sx),d(by,ty),d(sx,ty),1/2(d(ax,ty) + d(by,sx)) (3.1) then there is a Cauchy sequence in X beginning at x o defined by Y2n-I TX2n-i AX2n-2 Y2n SX2n BX2n-i for ncn the set of positive integers. PROOF. Since A(X)cT(X) B(X)cS(X) we can choose x x 2 in X such that Yl TXl AXo Y2 Sx2 BXl In general, we can choose X2n_l,X2n in X such that Y2n-1 TX2n-1 AX2n-2 Y2n SX2n BX2n-1 (3.2) Thus the indicated sequence exists. To see that is Cauchy, note that (3.1) (3.2) imply that d(tx2n+l,sx2n+2) d(ax2n,bx2n+l)_<r max(mn) where M n d(ax2n,sx2n) d(bx2n+ l,tx2n+ 1), d(sx2n,tx2n+l), 1/2(d(AX2n,TX2n+l) + d(bx2n+l,sx2n)) Then by (3.2) M n {d(tx2n+l,sx2n d(sx2n+2,tx2n+1 1/2d(SX2n+2,SX2n But 1/2d(SX2n+2,S2n)< 1/2(d(SX2n+2,TX2n+l + d(tx2n+l,sx2n))<_max d(sx2n+2,tx2n+l), d(tx2n+l,sx2n) since the larger of two numbers is greater or equal to their average. So we have max(mn) max {d(sx2n+2,tx2n+l), d(tx2n+l,sx2n)} with d(tx2n+l,sx2n+2) <_ r max(mn) But if d(tx2n+l,sx2n+2) <_ r d(tx2n/l,sx2n+2) d(tx2n/l,sx2n+2) 0 since r (0,1); thus max(mn) d(tx2n+l,sx2n) we conclude d(tx2n+l,sx2n/2)< r d(tx2n+l,sx2n) Similarly, d(tx2n+3,sx2n+2)! r d(sx2n+2,tx2n+l) Consequently, (3.2) implies that d(ym+l,ym)_< r d(ym,ym_ 1) for m even or odd. This last inequality implies that {Ym is Cauchy, as desired. / We shall also need the following simple result from [I (Proposition 2.2(2a)).
3 COMPATIBLE MAPPINGS AND COMMON FIXED POINTS 287 PROPOSITION 3.1. If f g are compatible self maps of a metric space (X,d) limnfxn limngx n t for some t in X then limngfx n ft if f is continuous. We can now state prove our generalization of Theorem I.I. THEOREM 3.1. Let A,B,S T be self maps of a complete metric space (X,d). Suppose that S T are continuous, the pairs A,S B,T are compatible, that A(X)(3 T(X) B(X) S(X). If there exists r (0,1) such that d(ax,by) < r max(mxy) for x,y in X where Mxy {d(ax,sx),d(by,ty),d(sx,ty), 1/2(d(ax,Ty) + d(by,sx))} (3.3) then there is a unique point z in X such that z Az Bz Sz Tz PROOF. By the Lemma 3.1. there is a sequence x n in X such that SX2n BX2n-I Y2n TX2n-I AX2n-2 Y2n-I such that the sequence Ym is Cauchy. Since (X,d) is complete {Ym converges to a point z in X Consequently, the subsequences AX2n SX2n,{ TX2n_l,{ BX2n_l converge to z (3.4) Since A S are compatible B T are compatible, the continuity of S T (3.4), Proposition 3.1. imply TTX2n_l,BTX2n_l Tz SSX2n,ASX2n Sz (3.5) Then (3.3) implies d(sz,tz) limnd(asx2n,btx2n_l)! r max(limm n) where M n {d(asx2n,ssx2n),d(btx2n_l,ttx2n_l),d(ssx2n,ttx2n_1), 1/2(d(ASX2n,TTX2n_ I) + d(ssx2n,btx2n_l)) }. By (3.5), lim n M {0,O,d(Sz,Tz),1/2(d(Sz,Tz) + n d(sz,tz)) so that d(sz,tz) r d(sz,tz) Since 0< r< Sz=Tz Also, d(az,tz) limnd(az,btx2n_l) r max(limnmn) where M n {d(az,sz) d(btx2n_l,ttx2n_l) d(sz,ttx2n_l), 1/2(d(Sz,BTX2n_1 + d(az,ttx2n_1)) Since Sz=Tz (3.5) yields" limnmn {d(az,tz),o,o,1/2(d(az,tz)) therefore, d(az,tz) < r d(az,tz) from which (as above) we infer Az=Tz(=Sz) But if we use this last stated equality in (3.3) with x=y=z we obtain" Az Bz Sz Tz (3.6) In fact, z is a common fixed point of A,B,S, T For (3.3) (3.4) yield" d(z,bz) limnd(ax2n,bz) r max(limnmn) with Mn d(ax2n,sx2n),d(bz,tz),d(sx2n,tz),1/2(d(ax2n,tz) + d(bz,sx2n))} Then limnmn {O,O,d(z,Tz),1/2(d(z,Bz) + d(bz,z))} by (3.4) (3.6). We thus
4 288 G. JUNGCK obtain d(z,bz) r d(z,bz) we conclude that z Bz Az Sz Tz That z is the only common fixed point of A,B,S, T follows easily from (3.3)./ We conclude with an example of four functions which satisfy the hypothesis of Theorem 3.1., no three of which satisfy the hypothesis of Theorem I.I.. EXAMPLE 3.1. Let X [I, ) d(x,y) x-y for x,y X Define Ax x Bx x Sx 2x 6 Tx 2x for x in X The functions are all continuous satisfy A(X)=B(X)-S(X)=T(X) X Moreover, Sx-Ax j2x + lj x 0 iff x since x ASx-SAx 6x(x-l) 0 iff x since x Thus, d(ax,sz) 0 only if x- in which instance d(asx,sax) 0 So A S are compatible; but they are not a weakly commuting hence not a commuting pair (Let x 2) Similarly, T B are compatible, since JTx-BxJ (2x+l)J x 0 iff x (x _>_ I) JTBx-BTxJ 2(x 1) 0 iff x (x >_ I) Finally, Sx-Tw 2J x y2 x: + y >_ 2J Ax-Bw 2 for x,y >_ I; therefore, Ax-ByJ J Sx-Tyj _< max(mxy) for x,y in X Hence (3.3), thus the hypothesis of Theorem 3.1., is satisfied. Observe also that no one of A,B,S, or T commutes with any two of the remaining three functions. Of course, common fixed point theorems other than Theorem I.I follow from Theorem See, for example, Corollary 3.2 of which in turn has Theorem I. of [5] as a corollary. REFERENCES I. Jungck, G. Compatible mappings common fixed points Internat. J_. Math. Math. Sci. _9(1936) 2. Park, S. Bae, Jong Sook Extensions of a fixed point theorem of Meir Keeler. Ark. Mat. 19(1981) Singh, S.L. Singh, S.P. A fixed point theorem. Indian J. Pure Ap_p. Math. I i(1980) Sessa, S. On a weak commutativity condition in fixed point considerations, Publ. Inst. Math. 3_2(46)(1982) Hadzic, Olga Common fixed point theorems for family of mapings in complete metric spaces. Math. Japonica 29(1984)
5 Journal of Applied Mathematics Decision Sciences Special Issue on Intelligent Computational Methods for Financial Engineering Call for Papers As a multidisciplinary field, financial engineering is becoming increasingly important in today s economic financial world, especially in areas such as portfolio management, asset valuation prediction, fraud detection, credit risk management. For example, in a credit risk context, the recently approved Basel II guidelines advise financial institutions to build comprehensible credit risk models in order to optimize their capital allocation policy. Computational methods are being intensively studied applied to improve the quality of the financial decisions that need to be made. Until now, computational methods models are central to the analysis of economic financial decisions. However, more more researchers have found that the financial environment is not ruled by mathematical distributions or statistical models. In such situations, some attempts have also been made to develop financial engineering models using intelligent computing approaches. For example, an artificial neural network (ANN) is a nonparametric estimation technique which does not make any distributional assumptions regarding the underlying asset. Instead, ANN approach develops a model using sets of unknown parameters lets the optimization routine seek the best fitting parameters to obtain the desired results. The main aim of this special issue is not to merely illustrate the superior performance of a new intelligent computational method, but also to demonstrate how it can be used effectively in a financial engineering environment to improve facilitate financial decision making. In this sense, the submissions should especially address how the results of estimated computational models (e.g., ANN, support vector machines, evolutionary algorithm, fuzzy models) can be used to develop intelligent, easy-to-use, /or comprehensible computational systems (e.g., decision support systems, agent-based system, web-based systems) This special issue will include (but not be limited to) the following topics: Computational methods: artificial intelligence, neural networks, evolutionary algorithms, fuzzy inference, hybrid learning, ensemble learning, cooperative learning, multiagent learning Application fields: asset valuation prediction, asset allocation portfolio selection, bankruptcy prediction, fraud detection, credit risk management Implementation aspects: decision support systems, expert systems, information systems, intelligent agents, web service, monitoring, deployment, implementation Authors should follow the Journal of Applied Mathematics Decision Sciences manuscript format described at the journal site Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at according to the following timetable: Manuscript Due December 1, 2008 First Round of Reviews March 1, 2009 Publication Date June 1, 2009 Guest Editors Lean Yu, AcademyofMathematicsSystemsScience, Chinese Academy of Sciences, Beijing , China; Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong; yulean@amss.ac.cn Shouyang Wang, AcademyofMathematicsSystems Science, Chinese Academy of Sciences, Beijing , China; sywang@amss.ac.cn K. K. Lai, Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong; mskklai@cityu.edu.hk Hindawi Publishing Corporation
fix- gx x +0 ff x 0 and fgx- gfxl 2x" 0 if x 0 so that f and g are compatible on R with the usual metric.
Internat. J. Math. & Math. Sci. VOL. Ii NO. 2 (1988) 285-288 285 COMPATIBLE MAPPINGS AND COMMON FIXED POINTS (2) GERALD JUNGCK Department of Mathematics Bradley University Peoria, Illinois 61625 (Received
More informationA NOTE ON THE HOMOMORPHISM THEOREM FOR HEMIRINGS
Internal. J. Math. & Math. Sci. Vol. (1978)439-445 439 A NOTE ON THE HOMOMORPHISM THEOREM FOR HEMIRINGS D. M. OLSON Department of Mathematics Cameron University Lawton, Oklahoma 73501 U.S.A. (Recieved
More informationle2 { Re d(a, f)l de > (1.2) n=2ar, 01 < e 2 ON ALPHA-CLOSE-TO-CONVEX FUNCTIONS OF ORDER BETA functions. f(z) z + z a n Re (1 ) zf + (I + zf"(z)) do >
Internat. J. Math. & Math. Sci. Vol. 9 No. 3 (1986) 435-438 435 ON ALPHA-CLOSE-TO-CONVEX FUNCTIONS OF ORDER BETA M.A. NASR Faculty of Science University of Mansoura Mansoura, Egypt (Received January 9,
More informationON THE CLASS OF QS-ALGEBRAS
IJMMS 2004:49, 2629 2639 PII. S0161171204309154 http://ijmms.hindawi.com Hindawi Publishing Corp. ON THE CLASS OF QS-ALGEBRAS MICHIRO KONDO Received 19 September 2003 We consider some fundamental properties
More informationON THE NORMALIZER OF A GROUP IN THE CAYLEY REPRESENTATION
Internat. J. Math. & Math. Sci. VOL. 12 NO. 3 (1989) 459-462 459 ON THE NORMALIZER OF A GROUP IN THE CAYLEY REPRESENTATION SURINDER K. SEHGAL Department of Mathematics The Ohio State University Columbus,
More informationCOUNTING OCCURRENCES OF 132 IN AN EVEN PERMUTATION
IJMMS 00:5, 139 131 PII. S016117103011 http://ijmms.hindawi.com Hindawi Publishing Corp. COUNTING OCCURRENCES OF 13 IN AN EVEN PERMUTATION TOUFIK MANSOUR Received 9 April 003 We study the generating function
More informationJACK-KANG CHAN. Norden Systems. 75 Maxess Road. Melville, New York Ax -b (1) det[a ix...i.; b: j] j 1,...,n det[a" ix...
Internat. J. Math. & Math. Sci. VOL. 15 NO. (1992) 41-46 41 A NOVEL INTERPRETATION OF LEAST SQUARES SOLUTION JACK-KANG CHAN Norden Systems 75 Maxess Road Melville, New York 11747 (Received March 5, 1991
More informationSome Results of Compatible Mapping in Metric Spaces
International Refereed Journal of Engineering and Science (IRJES) ISSN (Online) 2319-183X, (Print) 2319-1821 Volume 6, Issue 3 (March 2017), PP.38-44 Some Results of Compatible Mapping in Metric Spaces
More informationKENAN TA Department of Mathematics Abant Izzet Baysal University Bolu, 14280, TURKEY. MUSTAFA TELCl. Hacettepe University
Internat. J. Math. & Math. Sci. VOL. 9 NO. 3 (996) 45-456 45 COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS KENAN TA Department of Mathematics Abant Izzet Baysal University Bolu, 4280, TURKEY MUSTAFA
More informationPAijpam.eu COMMON FIXED POINT THEOREMS OF COMPATIBLE MAPPINGS IN METRIC SPACES
International Journal of Pure and Applied Mathematics Volume 84 No. 203, 7-83 ISSN: 3-8080 (printed version); ISSN: 34-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v84i.3
More informationJOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 5(3), Copyright c 2001, Lawrence Erlbaum Associates, Inc.
JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 5(3), 193 Copyright c 1, Lawrence Erlbaum Associates, Inc. Classroom Note Fourier Method for Laplace Transform Inversion M. IQBAL miqbal@kfupm.edu.sa
More informationA New Heuristic for the Quadratic Assignment Problem
JOURNAL OF APPLIED MATHEMATICS AND DECISION SCIENCES, 6(3), 143 153 Copyright c 2002, Lawrence Erlbaum Associates, Inc. A New Heuristic for the Quadratic Assignment Problem ZVI DREZNER zdrezner@fullerton.edu
More informationTHE FOURIER TRANSFORMS OF LIPSCHITZ FUNCTIONS ON CERTAIN DOMAINS
Internat. J. Math. & Math. Sci. VOL. 20 NO. 4 (1997) 817-822 817 THE FOURIER TRANSFORMS OF LISCHITZ FUNCTIONS ON CERTAIN DOMAINS M.S. YOUNIS Department of Mathematics Yarmouk University Irbid, JORDAN (Received
More informationCOMPATIBLE MAPPINGS AND COMMON FIXED POINTS
Internat. J. Math. & Math. Sci. Vol. 9 No. 4 (1986) 771-779 771 COMPATIBLE MAPPINGS AND COMMON FIXED POINTS GERALD JUNGCK Department of Mathematics Bradley University Peoria, lllinois 61625 (Received July
More informationWEAK SUB SEQUENTIAL CONTINUOUS MAPS IN NON ARCHIMEDEAN MENGER PM SPACE
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 7(2017), 65-72 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS
More informationA Common Fixed Point Theorem for Compatible Mappings of Type (K) in Intuitionistic Fuzzy Metric space
Journal of Mathematics System Science 5 (205) 474-479 oi: 0.7265/259-529/205..004 D DAVID PUBLISHING A Common Fixe Point Theorem for Compatible Mappings of Type (K) in K.B. Manhar K. Jha Department of
More informationFIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE
www.arpapress.com/volumes/vol10issue3/ijrras_10_3_11.pdf FIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE Bijendra Singh 1, Arihant Jain 2 and Javaid Ahmad Shah
More informationUNSTABLE K-COHOMOLOGY ALGEBRA IS FILTERED λ-ring
IJMMS 2003:10, 593 605 PII. S0161171203208012 http://ijmms.hindawi.com Hindawi Publishing Corp. UNSTABLE K-COHOMOLOGY ALGEBRA IS FILTERED λ-ring DONALD YAU Received 3 August 2002 Boardman, Johnson, and
More informationCOMMON FIXED POINT OF SEMI COMPATIBLE MAPS IN FUZZY METRIC SPACES
COMMON FIXED POINT OF SEMI COMPATIBLE MAPS IN FUZZY METRIC SPACES 1 M. S. Chauhan, 2 V. H. Badshah, 3 Virendra Singh Chouhan* 1 Department of Mathematics, Govt. Nehru PG College, Agar Malwa (India) 2 School
More informationCommon fixed point theorems in Menger space with special reference to coincidence points
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2015, 6(7):224-229 ISSN: 0976-8610 CODEN (USA): AASRFC Common fixed point theorems in Menger space with special
More informationGLOBAL PROPERTIES OF THE THREE-DIMENSIONAL PREDATOR-PREY LOTKA-VOLTERRA SYSTEMS
() Journal of Applied Mathematics & Decision Sciences, 3(2), 155-162 (1999) Reprints Available directly from the Editor. Printed in New Zealand. GLOBAL PROPERTIES OF THE THREE-DIMENSIONAL PREDATOR-PREY
More informationFixed Point Theorem in Fuzzy Metric Space Using (CLRg) Property
International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 5 Issue 4 April 2016 PP.35-39 Fixed Point Theorem in Fuzzy Metric Space Using (CLRg) Property
More informationREMARKS ON CERTAIN SELECTED FIXED POINT THEOREMS
IJMMS 29:1 (2002) 43 46 PII. S016117120200491X http://ijmms.hindawi.com Hindawi Publishing Corp. REMARKS ON CERTAIN SELECTED FIXED POINT THEOREMS M. IMDAD Received 8 July 1999 and in revised form 27 March
More informationFixed point theorems for generalized contraction mappings in multiplicative metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 237 2363 Research Article Fixed point theorems for generalized contraction mappings in multiplicative metric spaces Afrah A. N. Abdou
More informationCommon fixed points for compatible mappings in metric spaces
RADOVI MATEMATIČKI Vol. 12 (2003), 107 114 Common fixed points for compatible mappings in metric spaces K. Jha (Nepal), R.P. Pant and S.L. Singh (India) Abstract. In the present paper, a common fixed point
More informationCENTER CONDITIONS FOR A SIMPLE CLASS OF QUINTIC SYSTEMS
IJMMS 29:11 2002) 625 632 PII. S0161171202012802 http://ijmms.hindawi.com Hindawi Publishing Corp. CENTER CONDITIONS FOR A SIMPLE CLASS OF QUINTIC SYSTEMS EVGENII P. VOLOKITIN Received 13 April 2001 and
More informationJournal of Shivaji University (Science & Technology) SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION.
SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION. Deepti Thakur and Sushil Sharma Department of Mathematics, Madhav Vigyan Mahavidhyalaya, Vikram University, Ujjain
More informationCommon Fixed Point Theorems for Two Pairs of Weakly Compatible Mappings in Fuzzy Metric Spaces Using (CLR ST ) Property
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 6 Ver. I (Nov. - Dec.2016), PP 66-71 www.iosrjournals.org Common Fixed Point Theorems for Two Pairs of Weakly
More informationA Common Fixed Point Theorem Satisfying Integral Type Implicit Relations
Applied Mathematics E-Notes, 7(27, 222-228 c ISSN 167-251 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ A Common Fixed Point Theorem Satisfying Integral Type Implicit Relations Hemant
More informationAPPROXIMATING DISTRIBUTION FUNCTIONS BY ITERATED FUNCTION SYSTEMS
APPROXIMATING DISTRIBUTION FUNCTIONS BY ITERATED FUNCTION SYSTEMS STEFANO MARIA IACUS AND DAVIDE LA TORRE Received 1 August 2003 and in revised form 24 January 2004 An iterated function system (IFS) on
More information"Ixi. NONTRIVIAL ISOMETRIES ON Sp() llxll. Ip + I Ixi+I xi Ip" For i < p, p 2, 0 < a <, a # i, STEPHEN L. CAMPBELL. I nternat. J. Math. & Math. Sci.
I nternat. J. Math. & Math. Sci. Vol. 5 No. 2 (1982) 257-261 257 NONTRIVIAL ISOMETRIES ON S() STEHEN L. CAMBELL Deartment of Mathematics North Carolina State University Raleigh, North Carolina 27650 U.S.A.
More informationCOMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE
COMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE Latpate V.V. and Dolhare U.P. ACS College Gangakhed DSM College Jintur Abstract:-In this paper we prove common fixed point theorem
More informationCOMMON FIXED POINT THEOREM FOR SUB COMPATIBLE AND SUB SEQUENTIALLY CONTINUOUS MAPS IN FUZZY METRIC SPACE USING IMPLICT RELATION
IJRRAS 9 (1) October 011 www.arpapress.com/volumes/vol9issue1/ijrras_9_1_10.pdf COMMON FIXED POINT THEOREM FOR SUB COMPATIBLE AND SUB SEQUENTIALLY CONTINUOUS MAPS IN FUZZY METRIC SPACE USING IMPLICT RELATION
More informationIf(t-u) g(u) du. Department of Mathematics. (f*g)(t) KEY WORDS AND PHRASES. Abelian theorem, Boehmian, convolution, generalized
Internat. J. Math. & Math. Sci. VOL. 17 NO. 3 (1994) 489-496 489 ABELIAN THEOREMS FOR TRANSFORMABLE BOEHMIANS DENNIS NEMZER Department of Mathematics California State University, Stanislaus Turlock, California
More informationLEAN BUFFERING IN SERIAL PRODUCTION LINES WITH BERNOULLI MACHINES
LEAN BUFFERING IN SERIAL PRODUCTION LINES WITH BERNOULLI MACHINES A. B. HU AND S. M. MEERKOV Received 8 February 26; Accepted 7 April 26 Lean buffering is the smallest buffer capacity necessary to ensure
More informationGyeongsang National University
Internat. J. Math. & Math. Sci. VOL. 20 NO. 2 (1997) 249-256 249 COINCIDENCE THEOREMS FOR NONLINEAR HYBRID CONTRACTIONS Y.J. CHO B. FISHER G.S. GENGA Department of Mathematics and Computer Science Deptartment
More informationA Common Fixed Point Theorem for Self Mappings for Compatible Mappings of Type (E) in Fuzzy Metric space
Advances in Fuzzy Mathematics. ISSN 0973-533X Volume 11, Number 1 (2016), pp. 79-87 Research India Publications http://www.ripublication.com A Common Fixed Point Theorem for Self Mappings for Compatible
More informationOn Some Results in Fuzzy Metric Spaces
Theoretical Mathematics & Applications, vol.4, no.3, 2014, 79-89 ISSN: 1792-9687 (print), 1792-9709 (online) Scienpress Ltd, 2014 On Some Results in Fuzzy Metric Spaces Arihant Jain 1, V. H. Badshah 2
More informationWEAK SUB SEQUENTIAL CONTINUOUS MAPS IN NON ARCHIMEDEAN MENGER PM SPACE VIA C-CLASS FUNCTIONS
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 8(2018), 135-143 DOI: 10.7251/BIMVI1801135A Former BULLETIN
More informationSemi-Compatibility, Weak Compatibility and. Fixed Point Theorem in Fuzzy Metric Space
International Mathematical Forum, 5, 2010, no. 61, 3041-3051 Semi-Compatibility, Weak Compatibility and Fixed Point Theorem in Fuzzy Metric Space Bijendra Singh*, Arihant Jain** and Aijaz Ahmed Masoodi*
More informationFixed Point Theorems via Absorbing Maps
Thai Journal of Mathematics Volume 6 (2008) Number 1 : 49 60 www.math.science.cmu.ac.th/thaijournal Fixed Point Theorems via Absorbing Maps U. Mishra, A. S. Ranadive and D. Gopal Abstract : The purpose
More informationA Common Fixed Point Theorem for Compatible Mapping
ISSN 2224-386 (Paper) ISSN 2225-092 (Online) Vol., No., 20 A Common Fixed Point Theorem for Compatible Mapping Vishal Gupta * Department Of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala,
More informationAvailable online through ISSN
International Research Journal of Pure Algebra -4(3), 214, 426-431 Available online through www.rjpa.info ISSN 2248 937 A COMMON FIXED POINT THEOREM WITH INTEGRAL TYPE INEQUALITY Swati Choursiya* School
More informationAvailable online at Adv. Fixed Point Theory, 3 (2013), No. 4, ISSN:
Available online at http://scik.org Adv. Fixed Point Theory, 3 (2013), No. 4, 595-599 ISSN: 1927-6303 A COMMON FIXED POINT THEOREM UNDER ϕ-contractive CONDITIONS PH.R. SINGH 1,, AND M.R. SINGH 2, 1 Department
More informationCOMMON FIXED POINTS FOR COMPATIBLE MAPS ON THE UNIT INTERVAL
proceedings of the american mathematical society Volume 115, Number 2, June 1992 COMMON FIXED POINTS FOR COMPATIBLE MAPS ON THE UNIT INTERVAL GERALD JUNGCK (Communicated by James E. West) Abstract. Let
More informationC%. KEY WORDS AND PHRASES. Cantor set, midpoint set, distance set. C%, THE MIDPOINT SET OF A CANTOR SET. Internat. J. Math. & Math. Sci. KEN W.
Internat. J. Math. & Math. Sci. Vol. (1978)541-546 541 THE MIDPOINT SET OF A CANTOR SET KEN W. LEE Department of Mathematical Sciences Missouri Western State College 4525 Downs Drive Saint Joseph, Missouri
More informationA FIXED POINT THEOREM IN MENGER SPACES
International Mathematical Forum, 1, 2006, no. 32, 1543-1554 A FIXED POINT THEOREM IN MENGER SPACES Servet Kutukcu Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, Kurupelit,
More informationA Common Fixed Point Theorems in Menger Space using Occationally Weakly Compatible Mappings
A Common Fixed Point Theorems in Menger Space using Occationally Weakly Compatible Mappings Kamal Wadhwa, Jyoti Panthi and Ved Prakash Bhardwaj Govt. Narmada Mahavidyalaya, Hoshangabad, (M.P) India Abstract
More informationA Common Fixed Point Theorem in Intuitionistic Menger Spaces
International Journal on Recent Innovation Trends in Computing Communication ISSN: 2321-8169 A Common Fixed Point Theorem in Intuitionistic Menger Spaces Dr. Varsha Sharma Deptt. Of Mathematics Institute
More informationSOME RESULTS ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN COMPLETE METRIC SPACES
IJMMS 30:6 2002 319 325 PII. S0161171202110350 http://ijmms.hindawi.com Hindawi Publishing Corp. SOME RESULTS ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS IN COMPLETE METRIC SPACES JEONG SHEOK UME,
More informationCommon fixed point theorem for nonexpansive type single valued mappings
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 45-51 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.293 Common fixed point theorem for nonexpansive type single valued mappings Pankaj
More informationThus f is continuous at x 0. Matthew Straughn Math 402 Homework 6
Matthew Straughn Math 402 Homework 6 Homework 6 (p. 452) 14.3.3, 14.3.4, 14.3.5, 14.3.8 (p. 455) 14.4.3* (p. 458) 14.5.3 (p. 460) 14.6.1 (p. 472) 14.7.2* Lemma 1. If (f (n) ) converges uniformly to some
More informationFIXED POINT RESULTS IN SELF MAPPING FUNCTIONS
Int. J. Engg. Res. & Sci. & Tech. 2016 M Ramana Reddy, 2016 Research Paper ISSN 2319-5991 www.ijerst.com Vol. 5, No. 4, November 2016 2016 IJERST. All Rights Reserved FIXED POINT RESULTS IN SELF MAPPING
More informationWEAKLY COMPATIBLE MAPS IN FUZZY METRIC SPACES
WEAKLY COMPATIBLE MAPS IN FUZZY METRIC SPACES M. Rangamma, G. Mallikarjun Reddy*, P. Srikanth Rao Department of Mathematics,O.U.,Hyderabad. 500 007. *Corresponding address: mrcoolmallik@gmail.com Received
More informationCOMMON FIXED POINTS OF COMPATIBLE MAPS OF TYPE (β) ON FUZZY METRIC SPACES. Servet Kutukcu, Duran Turkoglu, and Cemil Yildiz
Commun. Korean Math. Soc. 21 (2006), No. 1, pp. 89 100 COMMON FIXED POINTS OF COMPATIBLE MAPS OF TYPE (β) ON FUZZY METRIC SPACES Servet Kutukcu, Duran Turkoglu, Cemil Yildiz Abstract. In this paper we
More informationWITH THE EFFECT OF GRAVITY
Internat. J. Math. & Math. Sci. VOL. 15 NO. 4 (1992) 795802 795 LAMB S PLANE PROBLEM IN A THERMOVISCOELASTIC MICROPOLAR MEDIUM WITH THE EFFECT OF GRAVITY PRAVANGSU SEKHAR OAS KTPP Township, Midnapore 721171,
More informationCommon fixed points of two maps in cone metric spaces
Rendiconti del Circolo Matematico di Palermo 57, 433 441 (2008) DOI: 10.1007/s12215-008-0032-5 Akbar Azam Muhammad Arshad Ismat Beg Common fixed points of two maps in cone metric spaces Received: July
More informationAvailable online at Advances in Fixed Point Theory, 2 (2012), No. 4, ISSN:
Available online at http://scik.org Advances in Fixed Point Theory, 2 (2012), No. 4, 452-463 ISSN: 1927-6303 SOME FIXED POINT RESULTS IN MENGER SPACES SUNNY CHAUHAN 1, SANDEEP BHATT 2, AND NEERAJ DHIMAN
More informationCommon Fixed Point Theorems for Six Mappings Satisfying Almost Generalized (S, T)-Contractive Condition in Partially Ordered Metric Spaces
Annals of Pure Applied Mathematics Vol. 1, No., 016, 143-151 ISSN: 79-087X (P), 79-0888(online) Published on 7 November 016 www.researchmathsci.org Annals of Common Fixed Point Theorems for Six Mappings
More informationOccasionally Weakly Compatible Mapping in Cone Metric Space
Applied Mathematical Sciences, Vol. 6, 2012, no. 55, 2711-2717 Occasionally Weakly Compatible Mapping in Cone Metric Space Arvind Bhatt Applied Science Department (Mathematics) Bipin trpathi Kumaun institute
More informationCommon fixed point theorems for four self maps on a fuzzy metric space, satisfying common E. A. property
Available online at www.pelagiaresearchlibrary.com Avances in Applie Science Research, 2015, 6(10): 35-39 ISSN: 0976-8610 CDEN (SA): AASRFC Common fixe point theorems for four self maps on a fuzzy metric
More informationSEMI COMPATIBILITY AND COMMON FIXED POINT THEOREM IN FUZZY METRIC SPACE USING IMPLICIT RELATION
International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Emerging Technologies in Computational
More informationCOMMON FIXED POINT THEOREM FOR SIX MAPPINGS ON FUZZY METRIC SPACES
TWMS J. Pure Appl. Math. V.6, N.2, 2015, pp.213-223 COMMON FIXED POINT THEOREM FOR SIX MAPPINGS ON FUZZY METRIC SPACES BHAVANA DESHPANDE 1, ROHIT PATHAK 2 Abstract. In this paper we extend the result of
More informationA Common Fixed Point Result in Complex Valued b-metric Spaces under Contractive Condition
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 4869-4876 Research India Publications http://www.ripublication.com A Common Fixed Point Result in Complex
More informationCommon Fixed Point Theorem in Fuzzy Metric. Space Using Implicit Relation
International Mathematical Forum, 4, 2009, no. 3, 135-141 Common Fixed Point Theorem in Fuzzy Metric Space Using Implicit Relation Suman Jain*, Bhawna Mundra** and Sangita Aske*** * Department of Mathematics,
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011
Common fixed point theorem for R weakly commutativity of type (Ag) satisfying general contractive type condition Anju Rani, Seema Mehra, Savita Rathee Department of Mathematics, M.D.University, Rohtak
More informationA COMMON FIXED POINT THEOREM FOR SIX MAPPINGS WITH A NEW BINARY OPERATOR
International Journal of Latest Trends in Engineering and Technology Vol.(8)Issue(), pp.60-608 DOI: http://dx.doi.org/0.7/.8.079 e-issn:78-6x A COMMON FIXED POINT THEOREM FOR SIX MAPPINGS WITH A NEW BINARY
More informationCommon Fixed Point Theorem for Six Maps in. d-complete Topological Spaces
Int. Journal of Math. Analysis, Vol. 6, 202, no. 4, 204-2047 Common Fixed Point Theorem for Six Maps in d-complete Topological Spaces Rahul Tiwari Department of Mathematical Sciences A.P.S. University,
More informationA fixed point theorem on compact metric space using hybrid generalized ϕ - weak contraction
Theoretical Mathematics & Applications, vol. 4, no. 4, 04, 9-8 ISSN: 79-9687 (print), 79-9709 (online) Scienpress Ltd, 04 A fixed point theorem on compact metric space using hybrid generalized ϕ - weak
More informationCommon Fixed Point Theorems for Generalized (ψ, φ)-type Contactive Mappings on Metric Spaces
Applied Mathematical Sciences, Vol. 7, 2013, no. 75, 3703-3713 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.35273 Common Fixed Point Theorems for Generalized (ψ, φ)-type Contactive
More informationMultiplicative metric spaces and contractions of rational type
Advances in the Theory of Nonlinear Analysis and its Applications 2 (2018) No. 4, 195 201. https://doi.org/10.31197/atnaa.481995 Available online at www.atnaa.org Research Article Multiplicative metric
More informationCommon fixed point theorems for pairs of single and multivalued D-maps satisfying an integral type
Annales Mathematicae et Informaticae 35 (8p. 43 59 http://www.ektf.hu/ami Common fixed point theorems for pairs of single and multivalued D-maps satisfying an integral type H. Bouhadjera A. Djoudi Laboratoire
More informationA Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity
Mathematica Moravica Vol. 10 (2006), 55 60 A Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity I. Kubiaczyk and Bhavana Deshpande Abstract. In this paper, we prove a common
More informationCommon Fixed Point Theorems for Compatible Mappings in Dislocated Metric Space
International Journal of Mathematical Analysis Vol. 9, 2015, no. 45, 2235-2242 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.57177 Common Fixed Point Theorems for Compatible Mappings
More informationResearch Article Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding
Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2008, Article ID 369125, 15 pages doi:10.1155/2008/369125 Research Article Adjoint Variable Method for the Study of Combined Active
More informationCOMMON FIXED POINTS OF COMPATIBLE MAPPINGS
Iterat. J. Math. & Math. Sci. VOL. 13 NO. (1990) 61-66 61 COMMON FIXED POINTS OF COMPATIBLE MAPPINGS S.M. KANG ad Y.J. CHO Departmet of Mathematics Gyeogsag Natioal Uiversity Jiju 660-70 Korea G. JUNGCK
More informationCOMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY
Novi Sad J. Math. Vol. 36, No. 1, 006, 75-86 COMMON FIXED POINT THEOREMS FOR FOUR MAPPINGS WITH SOME WEAK CONDITIONS OF COMMUTATIVITY Duran Turkoglu 1, Ishak Altun 1, Brian Fisher Abstract. Some results
More informationAvailable online at Advances in Fixed Point Theory, 3 (2013), No. 3, ISSN:
Available online at http://scik.org Advances in Fixed Point Theory, 3 (2013), No. 3, 493-501 ISSN: 1927-6303 A COMMON FIXED POINT THEOREM FOR WEAKLY COMPATIBLE MAPPINGS IN MENGER PM-SPACES M. SHARMA, R.C.
More informationCOMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE
Kragujevac Journal of Mathematics Volume 35 Number 3 (2011), Pages 463 470. COMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE B. D. PANT, SUNNY CHAUHAN AND QAMAR ALAM Abstract. The notion of weakly
More informationSome Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces
Mathematica Moravica Vol. 17-1 (013) 5 37 Some Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces Amit Singh B. Fisher and R.C. Dimri Abstract. In this paper we prove some fixed point
More informationarxiv: v1 [math.gm] 20 Oct 2014
arxiv:1410.5748v1 [math.gm] 20 Oct 2014 A CHARACTERIZATION OF CAUCHY SEQUENCES IN FUZZY METRIC SPACES AND ITS APPLICATION TO FUZZY FIXED POINT THEORY MORTAZA ABTAHI Abstract. We introduce the concept of
More informationCommon Fixed Point Theorem in Compact D Metric Spaces
International Mathematical orum, Vol. 6, 2011, no. 13, 605-612 Common ixed Point Theorem in Compact Metric Spaces 1 Nguyen Van Luong and 2 Nguyen Xuan Thuan epartment of Natural Sciences Hong uc University,
More informationInvariant Approximation Results of Generalized Contractive Mappings
Filomat 30:14 (016), 3875 3883 DOI 10.98/FIL1614875C Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Invariant Approximation Results
More informationFIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES. 1. Introduction and preliminaries
Asia Pacific Journal of Mathematics, Vol. 1, No. 1 (2014), 67-85 ISSN 2357-2205 FIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES ANIMESH GUPTA Department of Applied Mathematics, Vidhyapeeth
More informationFIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY. 1. Introduction. Novi Sad J. Math. Vol. 36, No. 1, 2006, 11-19
Novi Sad J Math Vol 36, No 1, 2006, 11-19 FIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY Bijendra Singh 1, Shobha Jain 2, Shishir Jain 3 Abstract The objective of this paper is to introduce
More informationA Common Fixed Point Theorem for Sub Compatibility and Occasionally Weak Compatibility in Intuitionistic Fuzzy Metric Spaces
Gen. Math. Notes, Vol. 21, No. 1, March 2014, pp. 73-85 ISSN 2219-7184; Copyright ICSRS Publication, 2014 www.i-csrs.org Available free online at http://www.geman.in A Common Fixed Point Theorem for Sub
More informationCOUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
Kragujevac Journal of Mathematics Volume 382 2014, Pages 249 257. COUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES STOJAN RADENOVIĆ Abstract. In this paper, by reducing
More informationFixed point theorems for a class of maps in normed Boolean vector spaces
RESEARCH Fixed point theorems for a class of maps in normed Boolean vector spaces Swaminath Mishra 1, Rajendra Pant 1* and Venkat Murali 2 Open Access * Correspondence: pant. rajendra@gmail.com 1 Department
More informationCommon Fixed Point Theorem for Six Mappings
Global Journal of Pure an Applie Mathematics. ISSN 0973-1768 Volume 13 Number (017) pp. 43-49 Research Inia Publications http://www.ripublication.com Common Fixe Point Theorem for Six Mappings Qamrul Haque
More informationSOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION. Ishak Altun and Duran Turkoglu
TAIWANESE JOURNAL O MATHEMATICS Vol. 13, No. 4, pp. 1291-134, August 29 This paper is available online at http://www.tjm.nsysu.edu.tw/ SOME IXED POINT THEOREMS OR WEAKLY COMPATIBLE MAPPINGS SATISYING AN
More informationAPPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED. Sungsik Yun
Korean J. Math. 3 05, No. 3, pp. 393 399 http://dx.doi.org/0.568/kjm.05.3.3.393 APPROXIMATE ADDITIVE MAPPINGS IN -BANACH SPACES AND RELATED TOPICS: REVISITED Sungsik Yun Abstract. W. Park [J. Math. Anal.
More information[Shrivastava, 5(10): October 2018] ISSN DOI /zenodo Impact Factor
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES COMMON FIXED POINT THEOREM IN INTUITIONISTICFUZZY METRIC SPACE USING IMPLICIT RELATIONS Rajesh Shrivastava* 1, Arihant Jain 2 & Amit Kumar Gupta 1 *1
More informationCommon Fixed Point Theorems for Generalisation of R-Weak Commutativity
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728,p-ISSN: 2319-765X, Volume 8, Issue 4 (Sep. - Oct. 2013), PP 09-13 Common Fixed Point Theorems for Generalisation of R-Weak Commutativity T. R. Vijayan,
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 5, Issue 1, July 2015
Semi Compatibility and Weak Compatibility in Fuzzy Metric Space and Fixed Point Theorems Chandrajeet Singh Yadav Vadodara Institute of Engineering, Vadodara (Gujarat) For all x, y, zx and s, t 0, Abstract:
More informationT,(V,,)=eU v. )KF and m I + )K + F K (1.2) T,(V,,) is the BUNDLE OF ORDER 2. (Received Febraury 21, 1991 and in revised form March 29, 1991)
Internat. J. Math. & Math. Sci. VOL. 16 NO. (1993) 201-204 PROLONGATIONS OF F-STRUCTURE TO. THE TANGENT BUNDLE OF ORDER 2 LOVEJOY S. DAS 201 Department of Mathematics Kent State University, Tuscarawas
More informationON T-FUZZY GROUPS. Inheung Chon
Kangweon-Kyungki Math. Jour. 9 (2001), No. 2, pp. 149 156 ON T-FUZZY GROUPS Inheung Chon Abstract. We characterize some properties of t-fuzzy groups and t-fuzzy invariant groups and represent every subgroup
More informationCOINCIDENCE AND COMMON FIXED POINT THEOREMS FOR FAINTLY COMPATIBLE MAPS
TWMS J. App. Eng. Math. V.7, N.1, 2017, pp. 25-32 COINCIDENCE AND COMMON FIXED POINT THEOREMS FOR FAINTLY COMPATIBLE MAPS ANITA TOMAR 1, SHIVANGI UPADHYAY 1, Abstract. The paper is aimed to generalize
More informationFixed Point Result for P-1 Compatible in Fuzzy Menger Space
Asian Journal of uzzy and Applied Mathematics (ISSN: 2321 564X) Volume 02 Issue 01, ebruary 2014 ixed Point Result for P-1 Compatible in uzzy Menger Space Rashmi Pathak 1, Manoj Kumar Shukla 2, Surendra
More informationResearch Article Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID 746045, 15 pages doi:10.1155/2010/746045 Research Article Common Fixed Points of Weakly Contractive and Strongly
More informationHybrid Pairs of Mappings with Some Weaker Conditions in Consideration of Common Fixed Point on 2-Metric Spaces
Mathematica Moravica Vol. 16-2 (2012), 1 12 Hybrid Pairs of Mappings with Some Weaker Conditions in Consideration of Common Fixed Point on 2-Metric Spaces Bhavana Deshpande and Rohit Pathak Abstract. In
More information