We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both the sense Kramosil and Michalek George Veeramani by using new property give examples. Our results improve generalize main Mihet (Mihet, 2010) many spaces.

Recently, Azam et al. introduced new spaces called the complex valued metric and established existence of fixed point theorems under contraction condition. In this article, we extend improve condition results also apply main result to unique common solution system Urysohn integral equation. Mathematics Subject Classification (2000): 47H09; 47H10.

Abstract In this article, we study and prove the new existence theorems of fixed points for contraction mappings in modular metric spaces. AMS: 47H09; 47H10.

In this article the concept of coupled best proximity point and cyclic contraction pair are introduced then we study existence convergence these points in metric spaces. We also establish new results on a uniformly convex Banach Furthermore, give fixed spaces some illustrative examples. An open problems given at end for further investigation.

Abstract Coupled fixed point results for nonlinear contraction mappings having a mixed monotone property in partially ordered G -metric space due to Choudhury and Maity are extended unified. We also provide example validate the main this article. Mathematics Subject classification (2000) : 47H10; 54H25.

Abstract Recently, Gordji et al. [Math. Comput. Model. 54, 1897-1906 (2011)] prove the coupled coincidence point theorems for nonlinear contraction mappings satisfying commutative condition in intuitionistic fuzzy normed spaces. The aim of this article is to extend and improve some Also, we give an example a mapping which not applied by results al., but can be our results. 2000 MSC : primary 47H10; secondary 54H25; 34B15.

Abstract We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give unique result mapping cyclical condition. also provide illustrative examples. MSC: 47H10, 54H25.

Abstract In this paper, we show the existence of a coupled fixed point theorem nonlinear contraction mappings in complete metric spaces without mixed monotone property and give some examples mapping, which is not applied to by using property. We also study necessary condition for uniqueness given mapping. Further, apply our results mapping partially ordered spaces. Moreover, applications integral equations are presented. MSC: 47H10, 54H25.

In this article, we define a tangential property which can be used not only for single-valued mappings but also multi-valued mappings, and it in the prove existence of common fixed point theorems Gregus type four satisfying strict general contractive condition integral metric spaces. Our generalize unify main results Pathak Shahzad (Bull. Belg. Math. Soc. Simon Stevin 16, 277-288, 2009) several known results.

Abstract Recently, the complex-valued metric spaces which are more general than were first introduced by Azam et al. (Numer. Funct. Anal. Optim. 32:243-253, 2011). They also established existence of fixed point theorems under contraction condition in these spaces. The aim this paper is to introduce concepts a C -Cauchy sequence and -complete establish common Furthermore, we apply our result obtain theorem for solution Urysohn integral equations <mml:math...

In this paper, we prove a common fixed point theorem for pair of weakly compatible mappings in fuzzy metric space using the joint limit range property called (JCLR) property. An example is also furnished which demonstrates validity main result. We extend our result to two finite families self mappings. Our results improve and generalize Cho et al. [Y. J. Cho, S. Sedghi N. Shobe, “Generalized theorems with some types spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.]...

We extend the recent results of coupled fixed point theorems Cho et al. (2012) by weakening concept mixed monotone property. also give some examples a nonlinear contraction mapping, which is not applied to existence but can be our results. The main and unify many theorems.

This study investigates the intricacies of animal decision-making in T-maze environments through a synergistic approach combining computational modeling and machine learning techniques. Focusing on binary process T-mazes, we examine how animals navigate choices between two paths. Our research employs mathematical model tailored to behavior fish, offering analytical insights into their complex behavioral patterns. To complement this, apply advanced algorithms, specifically Support Vector...

The concept of tangential for single‐valued mappings is extended to multivalued and used prove the existence a common fixed point theorem Gregus type four satisfying strict general contractive condition integral type. Consequently, several known results generalized improved corresponding recent result Pathak Shahzad (2009) many authors.