Common Fixed Point Theorems for Four Self Maps on A Menger Space, Satisfying Common E. A. Property

In this paper, we prove common fixed point theorems for four self maps by using weak compatibility in Menger spaces. Our result extend, generalized several fixed point theorems on Menger spaces. Keywords— Common fixed points, Metric space, Menger space, weak compatible mappings and E. A. property. AMS subject classification– 47H10, 54H25

Common Fixed Point Theorems of Integral Type in Menger Pm Spaces

In this paper, we propose integral type common fixed point theorems in Menger spaces satisfying common property (E.A). Our results generalize several previously known results in Menger as well as metric spaces. Keywords: Menger space; Common property (E.A); weakly compatible pair of mappings and t-norm

Fixed Point Results In Fuzzy Menger Space With Rational Expression

This paper presents some common fixed point theorems for occasionally weakly compatible mappings with rational expression in Fuzzy menger metric spaces. Keywords: Occasionally weakly compatible mappings, Fuzzy menger metric space,Weak compatible mapping, Semi-compatible mapping, Implicit function, common fixed point. Subject Classification: AMS (2000) 47H2

Fixed Points of Weakly Compatible Mappings Using Common (E.A) Like property

The aim of this paper is to prove common fixed point theorems in Menger spaces using implicit relation and common (E.A) like property. An example is derived to support our main result. We extend our result to four finite families of self mappings. As an application of our main result, we prove an integral type common fixed point theorem satisfying ψ-contraction condition in Menger space. Our results improve some recent results in Menger spaces

Common Fixed Point Theory in Modified Intuitionistic Probabilistic Metric Spaces with Common Property (E.A.)

In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and  the common property (E.A.) in   modified  intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation

Some fixed point theorems for weakly compatible mappings in Non-Archimedean Menger probabilistic metric spaces via common limit range property

In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature

On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings

[EN] We present a procedure to construct a compatible metric from a given fuzzy metric space. We use this approach to obtain a characterization of a large class of complete fuzzy metric spaces by means of a fuzzy version of Caristi’s fixed point theorem, obtaining, in this way, partial solutions to a recent question posed in the literature. Some illustrative examples are also given.The authors thank the referees for several useful suggestions. Salvador Romaguera and Pedro Tirado acknowledge the support of the Ministry of Economy and Competitiveness of Spain, grant MTM2012-37894-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2015). On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings. Fixed Point Theory and Applications. 2015:226. https://doi.org/10.1186/s13663-015-0476-1S2015:226Kelley, JL: General Topology. Springer, New York (1955)Schweizer, B, Sklar, A: Statistical metric spaces. Pac. J. Math. 10, 314-334 (1960)Klement, E, Mesiar, R, Pap, E: Triangular Norms. Kluwer Academic, Dordrecht (2000)Hamacher, H: Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. In: Progress in Cybernetics and Systems Research, pp. 276-287. Hemisphere, New York (1975)Kramosil, I, Michalek, J: Fuzzy metrics and statistical metric spaces. Kybernetika 11, 326-334 (1975)George, A, Veeramani, P: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994)Gregori, V, Romaguera, S: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485-489 (2000)Radu, V: On the triangle inequality in PM-spaces. STPA, West University of Timişoara 39 (1978)Abbas, M, Ali, B, Romaguera, S: Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat 29(6), 1217-1222 (2015)Cho, YJ, Grabiec, M, Radu, V: On Nonsymmetric Topological and Probabilistic Structures. Nova Science Publishers, New York (2006)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Mihet, D: A note on Hicks type contractions on generalized Menger spaces. STPA, West University of Timişoara 133 (2002)Mihet, D: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431-439 (2004)Radu, V: Some fixed point theorems in PM spaces. In: Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol. 1233, pp. 125-133. Springer, Berlin (1985)Radu, V: Some remarks on the probabilistic contractions on fuzzy Menger spaces (The Eighth Intern. Conf. on Applied Mathematics and Computer Science, Cluj-Napoca, 2001). Autom. Comput. Appl. Math. 11(1), 125-131 (2002)Chauhan, S, Shatanawi, W, Kumar, S, Radenović, S: Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces. J. Nonlinear Sci. Appl. 7, 28-41 (2014)Hussain, N, Salimi, P, Parvaneh, V: Fixed point results for various contractions in parametric and fuzzy b-metric spaces. J. Nonlinear Sci. Appl. 8, 719-739 (2015)Mihet, D: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. J. Nonlinear Sci. Appl. 6, 35-40 (2013)Hicks, TL: Fixed point theory in probabilistic metric spaces. Zb. Rad. Prir.-Mat. Fak. (Novi Sad) 13, 63-72 (1983)Radu, V: Some suitable metrics on fuzzy metric spaces. Fixed Point Theory 5, 323-347 (2004)O’Regan, D, Saadati, R: Nonlinear contraction theorems in probabilistic spaces. Appl. Math. Comput. 195, 86-93 (2008)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed-point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Ansari, QH: Metric Spaces: Including Fixed Point Theory and Set-Valued Maps. Alpha Science, Oxford (2010

Unified common fixed point theorems under weak reciprocal continuity or without continuity

[EN] The purpose of this paper is two fold. Firstly, using the notion of weak reciprocal continuity due to Pant et al. Weak reciprocal continuity and fixed point theorems, Ann. Univ. Ferrara Sez. VII Sci. Mat. 57(1), 181-190 (2011)], we prove unified common fixed point theorems for various variants of compatible and $R$-weakly commuting mappings in complete metric spaces employing an implicit relation which covers a multitude of contraction conditions yielding thereby known as well as unknown results as corollaries. Secondly, we point out that more natural results can be proved under relatively tighter conditions if we replace the completeness of the space by completeness of suitable subspaces. The realized improvements in our results are also substantiated using appropriate examples.Kadelburg, Z.; Imdad, M.; Chauhan, S. (2014). Unified common fixed point theorems under weak reciprocal continuity or without continuity. Applied General Topology. 15(1):65-84. doi:10.4995/agt.2014.1823SWORD6584151J. Ali and M. Imdad, An implicit function implies several contraction conditions, Sarajevo J. Math. 4, no. 2 (2008), 269-285.S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181.B. C. Dhage, On common fixed points of coincidentally commuting mappings in $D$-metric spaces, Indian J. Pure Appl. Math. 30, no. 4 (1999), 395-406.Husain, S. A., & Sehgal, V. M. (1975). On common fixed points for a family of mappings. Bulletin of the Australian Mathematical Society, 13(2), 261-267. doi:10.1017/s000497270002445xM. Imdad and J. Ali, Reciprocal continuity and common fixed points of nonself mappings, Taiwanese J. Math. 13, no. 5 (2009), 1457-1473.Imdad, M., Ali, J., & Tanveer, M. (2009). Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces. Chaos, Solitons & Fractals, 42(5), 3121-3129. doi:10.1016/j.chaos.2009.04.017M. Imdad and Q. H. Khan, Six mappings satisfying a rational inequality, Rad. Mat. 9, no. 2 (1999), 251-260.Imdad, M., Khan, M. S., & Sessa, S. (1988). On some weak conditions of commutativity in common fixed point theorems. International Journal of Mathematics and Mathematical Sciences, 11(2), 289-296. doi:10.1155/s0161171288000353M. Imdad, S. Kumar and M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations. Rad. Mat. 11, no. 1 (2002), 135-143.Jungck, G. (1976). Commuting Mappings and Fixed Points. The American Mathematical Monthly, 83(4), 261. doi:10.2307/2318216Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9(4), 771-779. doi:10.1155/s0161171286000935G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29, no. 3 (1998), 227-238.M. S. Khan and M. Imdad, A common fixed point theorem for a class of mappings, Indian J. Pure Appl. Math. 14 (1983), 1220-1227.S. Kumar and R. Chugh, Common fixed points theorem using minimal commutativity and reciprocal continuity conditions in metric space, Sci. Math. Japon. 56, no. 2 (2002), 269-275.Murthy, P. P. (2001). Important tools and possible applications of metric fixed point theory. Nonlinear Analysis: Theory, Methods & Applications, 47(5), 3479-3490. doi:10.1016/s0362-546x(01)00465-5Pant, R. P. (1994). Common Fixed Points of Noncommuting Mappings. Journal of Mathematical Analysis and Applications, 188(2), 436-440. doi:10.1006/jmaa.1994.1437R. P. Pant, Common fixed points of four mappings, Bull. Cal. Math. Soc. 90 (1998), 281-286.R. P. Pant, Noncompatible mappings and common fixed points, Soochow J. Math. 26 (2000), 29-35.Pant, R. P., Bisht, R. K., & Arora, D. (2011). Weak reciprocal continuity and fixed point theorems. ANNALI DELL’UNIVERSITA’ DI FERRARA, 57(1), 181-190. doi:10.1007/s11565-011-0119-3H. K. Pathak, Y. J. Cho and S. M. Kang, Remarks on $R$-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc. 34, no. 2 (1997), 247-257.H. K. Pathak and M. S. Khan, A comparison of various types of compatible maps and common fixed points, Indian J. Pure Appl. Math. 28, no. 4 (1997), 477-485.V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32, no. 1 (1999), 157-163.V. Popa, M. Imdad and J. Ali, Fixed point theorems for a class of mappings governed by strictly contractive implicit function, Southeast Asian Bulletin of Math. 34, no. 5 (2010), 941-952.S. L. Singh and A. Tomar, Weaker forms of commuting maps and existence of fixed points, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 10, no. 3 (2003), 145-161