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In the present paper, we proved a common fixed-point theorem for two-hybrid pair of non-self mappings satisfying a generalized $(F, \xi, \eta) $- contraction condition under joint common limit range property in weak partial $b$- metric spaces. Our result is a generalization of many works available in metric space setting. An example and application to the integral equation are given to support the results proved in this paper.

In this paper, first, we deal with new metric space Sm-metric space that combines multiplicative metric space and S-metric space. We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC). We are also studying the well-posedness of Sm metric space. Further, some examples are presented to support our outcome.

In this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.

In this paper, we introduce a new class of contractive mapping in intuitionistic fuzzy metric space (IFMS). We establish fixed point theorems under such contractive mapping in complete IFMS and prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in IFMS.

In this paper, we firstly introduce a new notion of inverse C k − class functions which extends the notion of inverse C − class functions introduced by Saleem et al., 2018. Secondly, some common fixed point theorems are stated under some compatible conditions such as weak semicompatible of type A , weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called S τ − compatibility which is weaker than E . A . property and also present a common fixed point theorem in metric spaces via inverse C k − class functions. Some examples are provided to support our results.

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

Recently, the concept of Ƒ metric space has been introduced and have been defined a natural topology in this spaces by Jleli and Samet[6]. Furthermore, a new style of Banach contraction principle has been given in the Ƒ metric spaces. In this paper, we prove some coincidence and common fixed point theorems in Ƒ metric spaces.

The main objective of this paper is to present a common fixedpoint theorem for two pairs of single and set valued mappings via subsequentialcontinuity and \delta- compatibility. To illustrate the validity of our results, anexample is provided and we give also an application for a system of integralinclusions of Volterra type.

In this paper we prove existence and uniqueness of a common fixed point for non-self coincidentally commuting mappings with nonlinear, generalized contractive condition defined on strictly convex Menger PM-spaces proved.

Objective/Aim: To establish the existence of common fixed point theorem for four self-mappings in Banach space. Method: This method includes using weaker conditions like property E.A and weakly compatible mappings. Findings: Unique common fixed point is generated using different conditions. This result is supported by the provision of a suitable example.Novelty/Improvement: The concept of property E.A along with weakly compatible mappings is employed and is weaker than the concept of continuity and compatibility. Keywords: Fixed point; metric space; Normed space; Banach space; EA property; weakly compatible mappings

The main target of this paper have been to apply the concept of probabilistically convexity on menger space and deal a common fixed point theorem by using the concept of compatibility between multi-valued mappings and self mappings in the above context. All the results are the generalization of aforesaid paper of Rhoades (9, 10) Som and Mukherjee (12), Iseki (6), Chang et al. (4) and Lee (8).

The objective of this paper is to establish a theorem involving a pair of weakly compatible mappings fulfilling a contractive condition of rational type in the context of dislocated quasi metric space. Besides we proved the existence and uniqueness of coupled coincidence and coupled common fixed point for such mappings. This work offers extension as well as considerable improvement of some results in the existing literature. Lastly, an illustrative example is given to validate our newly proved results.

In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results.

Our aim of this paper is to prove a new general common fixed point theorem for two pair of mappings under a different set of conditions using the idea of weakly compatible mappings satisfying a general class of contractions defined by an implicit relation in the frame work of parametric metric space, which unify, extend and generalize most of the existing relevant common fixed point theorems from the literature. Some related results and illustrative an example to highlight the realized improvements is also furnished.

In this paper, we introduce generalized weakly contractive mappings in the setting of multiplicative metric spaces. Further we establish a common fixed point result and proved the existence and uniqueness of a common fixed point. Finally, we provide an example in support of our main finding.

In this paper, we prove some unique common fixed point theorem for two pairs of weakly compatible mappings, satisfying the rational contraction conditions in complex valued metric space. The proved result, generalize and extend some known results in the literature. Finally, The main result is the application of the Urysohn integral equations to derive the existence theorem for a general solution. AMS(MOS) Subject Classification Codes: 47H10, 54H25.

In this paper, we propose the notion of $$(\psi ,\phi )$$ -Wardowski contraction pairs and achieve a common fixed point theorem consistent with such kind of contractions in complete metric spaces. One of the main motivations of this article is to define a contractive condition which does not compel the mappings to be continuous at their common fixed points, an interesting question posed by Rhoades (Contemporary Math 72:233–245, 1988). Besides, we provide some applications of our obtained results in certain type of operator equations, fractional differential equation boundary value problems, functional equations arising in dynamic programmings, and a particular type of non-linear quadratic integral equations which are relevant to events arising in physics, economics, engineering, operations research, and many other relevant disciplines.

In this paper, we prove a common fixed point theorem for four pairs of mappings which satisfy the E . A - property in b - metric spaces. The proposed theorem expands and generalizes several well-known comparable results in the literature. Example is given showing that our result is proper extensions of the existing ones. Obtained results are useful in solving Mechanical problems as well as in image processing and deep learning. The established results satisfy the previous well known results.

In this article, some coupled coincidence point results for two mappings g: X → X and G: X × X → X satisfying F-contractive type conditions are obtained, and some coupled fixed point results are derived in partially ordered metric spaces. A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction, and a coupled common fixed point theorem is obtained. Some examples are given to support our results.

In this paper, we study some cases of a common fixed point theorem for classes of firmly nonexpansive and generalized nonexpansive maps. In addition, we establish that the Picard-Mann iteration is faster than Noor iteration and we used Noor iteration to find the solution of delay differential equation.

The concept of 2-metric space and b-metric space. Mustafa et. al. (Z. Mustafa. V, Paraneh, J. Razaei and Z. Kadulberg: b2 -metric spaces and some fixed point theorems, Fixed Point Theory and Applications 2014, 2014:144) introduced b2 -metric space are generalised. In this paper, we prove a common fixed point theorem for two pairs of weakly compatible mappings satisfying (\(\varphi\), \(\psi\)) contractive condition in b2 -metric space.

The purpose of this paper is to introduce and study a concept, called F-contraction mappings which generalize Lipschtzian mappings. They form a class that is wider than the Lipschtzian mappings. Moreover, we establish a new approach to obtain a common fixed point theorem for two commuting mappings, in order to get an equivalent theorem to G. Jungck’s result (Am Math Mon 83:261–263, 1976). Our result is illustrated by examples and generalizes Banach contraction theorem. The two joined theorems of both G. Jungck and ours are realised and some applications in the ball are derived from.

This paper is aimed at proving a common fixed point theorem for F -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich&ndash, Rus&ndash, Ćirić type contraction and Hardy&ndash, Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

This In this paper, we define new control functions to give unique fixed point in fuzzy metric space. A fruitful contractive condition of (ψ, ϕ)- type is used to obtain common fixed point theorem for two maps in fuzzy metric spaces. We extend the existing results in metric space to fuzzy metric space using these control functions. The first theorem is the extension of the result of Zhang and Song (2009) under the required contractive conditions. Second result is analogous to the result of Doric (2009) in metric spaces.