$f$-contraction

In this paper, we consider a new extension of the Banach contraction principle, $\theta$-$\Omega$-contraction inspired by the concept of $\theta$-contraction in $(\alpha,\eta )$-$b$-rectangular metric spaces to study the existence and uniqueness of fixed point theorems for the mappings in metric spaces. Moreover, we discuss some illustrative examples to highlight the realized improvements.

The available literature shows that the ideas of admissible mappings and that of Suzuki-type contractions on metric spaces have been well-investigated. However, a hybrid version of these results in connection with $\theta$-contraction has not been adequately examined. On this basis therefore, the aim of this paper is to introduce a new concept under the name an admissible Jaggi-Suzuki-type hybrid ($\theta$-$\phi$)-contraction and to study new conditions for the existence of fixed point for this class of contractions on generalized or rectangular metric space. Applications and examples are provided to support the assumptions of our  presented theorems. The results established herein extend some existing ideas in the corresponding literature. A few of these special cases are highlighted and discussed as corollaries.

In this paper, we improve the previous results from fixed point theory related to four types of contractions: interpolative Kannan contraction, extended interpolative and Geraghty type contraction, interpolative Hardy-Rogers contraction and Wardowski F-contraction. The basis for our generalization is the results from ``Extended Interpolative Hardy-Rogers-Geraghty-Wardowski Contractions and an Application'' as well as ``On extended interpolative \'{C}iri\'{c}-Reich-Rus type F-contractions and an application''.

In this paper, a collection of various multi-valued fixed point results using Feng-Liu operator on metric space are examined. Comparative discussion on some of the important ideas, using this operators are presented. Thereafter the handful of potential improvements on the existing literature are proposed.

‎In this paper‎, ‎we established the Boyd-Wong type and Meir-Keeler type contractions in a new generalized b-metric space‎.‎Two types of fixed point theorems are proven‎, ‎which extend the same results in the metric and b-metric spaces‎. ‎Some examples and an application are also discussed to show the applicability of the results‎.

‎This manuscript studies new concepts of hybrid $F$-contractions on a complete metric space‎. ‎It provides new conditions for the existence of fixed points for such mappings‎. ‎The main idea of this paper unifies a few important results in the corresponding literature‎. ‎Some of these consequences are highlighted and discussed as corollaries‎. ‎In support of the assumptions forming the theorems presented herein‎, ‎a comparative nontrivial example with a graphical illustration is provided‎.

In this attend, a new weakly singular fractional integral equation is presented. Under the suitable control conditions on parameters, we prove a existence solution theorem for the proposed equation. Finally, some examples are given and with the help of MATLAB R2018a parameters is finding.

In the setting of uniformly convex Banach spaces equipped with a partially ordered relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of Alfuraidan and Khamsi [M. R. Alfuraidan, M. A. Khamsi, Proc. Amer. Math. Soc., 146, (2018), 2451-2456]. Examples are given to show the usability of our main conclusions. We also study the existence of an optimal solution for cyclic contractions in such spaces.

Our present work is the extension of the line of research in the context of $\phi$-metric spaces. We introduce the notion of fixed circle and obtain suitable conditions for the existence and uniqueness of fixed circles for self mappings. Additionally, we present some figures and examples in support of our  results.

In this article, we define  generalized $(\varphi,\sigma,\gamma)$-rational contraction, generalized $(\alpha\beta,\varphi\theta,F)$-rational  contraction  and establish some new fixed  point results in $(\phi,\psi)$-metric space. We also present instances to support our main results. We will use the results we obtained to investigate the existence and uniqueness of solutions to first-order differential equations.

In this work, a collection of various fixed point results of $\Theta$-contractions are examined. Important results from when the concept was introduced up to the recent developments are discussed. Hence, the aim of this paper is to collate and analyze the advances of fixed point results in the setting of $\Theta$-contractions which will be helpful and handy for researchers in fixed point theory and related domains.

The search for contractive definitions which do not compel the mapping to be continuous at fixed points remained an open problem for a long time. Several solutions to this open problem have been obtained in last two decades. The current paper,  we aim to provide another new solution direction for the discontinuity study  at fixed points using $F$-contractive mappings in a complete metric space. Several consequences of those new results are also provided. This manuscript consists of three main parts. In the first part, the notion of $F$-contractive mappings has been described. In the second part, discontinuity at the fixed point assuming continuity of the composition has been investigated, whereas in the third part, discontinuity at a fixed point without assuming continuity of the composition has been illustrated.

In this manuscript, we introduce new notions of generalized ($\mathfrak{f^{*}}, \psi)$-contraction and utilize this concept to prove some fixed point results for lower semi-continuous $\psi$-mapping satisfying certain conditions in the frame of G-metric spaces. Our results improve the results of [6] and [8] by omitting the continuity condition of $F\in \Im$ with the aid of the $\psi$-fixed point. We give an illustrative example to help accessibility of the got results and to show the genuineness of our results. Also, many existing results in the frame of metric spaces are established. Moreover, as an application, we employ the achieved result to earn the existence and uniqueness criteria of the solution of a type of non-linear integral equation.

In this manuscript, we introduce generalized orthogonal ($\mathfrak{f^{*}}, \psi)$-contraction of kind (S) and use this concept to establish $\psi$-fixed point theorems in the frame of O-complete orthogonal metric space. Secondly, we introduce the new notion of generalized orthogonal ($\mathfrak{f^{*}}, \psi)$ expansive mapping and utilize the same to prove some fixed point results for surjective mapping satisfying certain conditions. Our results extend and improve the results of  [3] and [7] by omitting the continuity condition of $F\in \Im$ with the aid of $\psi$-fixed point. We also give an illustrative example which yields the main result. Also, many existing results in the frame of metric spaces are established.

Owing to the notion of L-fuzzy mapping, we establish some common $L$-fuzzy fixed point results for almost $\Theta$-contraction in the setting of complete metric spaces. An application to theoretical computer science is also provided to show the significance of the investigations.

In this paper, we further develop the notion of cyclic $(\alpha, \beta)$-admissible mappings introduced in (\cite{tac}, S. Chandok, K. Tas, A. H. Ansari, \emph{Some fixed point results for TAC-type contractive mappings,} J. Function spaces, 2016, Article ID 1907676, 1--6) and $(\psi, F)$-contraction mappings introduced in ( \cite{wad1}, D. Wardowski, \emph{Solving existence problems via $F$-contractions,} Proceedings of the American Mathematical Society, 146 (4), (2018), 1585--1598), in the framework of $b$-metric spaces. To achieve this, we introduce the notion of $(\alpha,\beta)-S$-admissible mappings and a new class of generalized $(\psi, F)$-contraction types and establish a common fixed point and fixed point results for these classes of mappings in the framework of complete $b$-metric spaces. As an application, we establish the existence and uniqueness of the solutions to differential equations in the framework of fractional derivatives involving Mittag-Leffler kernels via the fixed point technique. The results obtained in this work provide extension as well as substantial generalization and improvement of the fixed point results obtained in \cite{tac,wad1, wad} and several well-known results on fixed point theory and its applications.

In this paper, we present some fixed point results for cyclic weak $\phi$-contractions in $\omega$-complete modular metric spaces and $\omega$-compact modular metric spaces, respectively. Some results for contractions that have zero cyclic properties are also provided.

‎In the present work‎, ‎Banach and Kannan integral type contractions in metric spaces endowed with a graph are considered and‎ ‎the existence and uniqueness of best proximity points for mappings satisfying in these contractions are proved‎.

We investigate the mechanisms of dynamic technique to rational type contraction in the context of partially ordered metric spaces and obtain coupled fixed points in this article. Our derived results extend and generalize some prominent outcomes in the literature. At last, we have produced an example and an application for a system of integral that preserve the main results.

In the present paper, we establish some generalized cyclic contraction results through $p$-number of subsets by using two different types of t-norm, viz. Hadzic type t-norm and minimum t-norm in the setting of 2- probabilistic metric spaces. Our results generalize some existing fixed point theorems in 2-Menger spaces. Some illustrative examples and an application to the existence of a solution to Airy’s type differential equation are also provided.