θ*-Weak Contractions and Discontinuity at the Fixed Point with Applications to Matrix and Integral Equations

In this paper, the notion of θ*-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan and Rhoades on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

θ∗-Weak Contractions and Discontinuity at the Fixed Point With Applications to Matrix and Integral Equations

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

Fixed point results for weak contractions in partially ordered b-metric space

Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

Set-valued Contractions in b-Metric Spaces with Application

In this article, we present a (α, F)-set-valued mapping in setting b-metric space by characterizing the weak contraction condition with the C function and the α-set-valued function of type S. There are examples and implementations accessible that illustrate the validity of our findings.

Fixed Point of Generalized Weak Contraction in b -Metric Spaces

In this manuscript, a class of generalized ψ , α , β -weak contraction is introduced and some fixed point theorems in the framework of b -metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.

Cyclic G ‐ Ω -Weak Contraction-Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces

This paper introduces novel concepts of joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak contraction and joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G ‐ Ω S , a b e f -weak contraction and cyclic G ‐ Ω S , a b e f -weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic Ω S , a b e f -weak contraction and cyclic Ω S , a b e f -weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

On Unique and Nonunique Fixed Points in Metric Spaces and Application to Chemical Sciences

We introduce the notions of a generalized Θ -contraction, a generalized Θ E -weak contraction, a Ψ E -weak JS-contraction, an integral-type Θ E -weak contraction, and an integral-type Ψ E -weak JS-contraction to establish the fixed point, fixed ellipse, and fixed elliptic disc theorems. Further, we verify these by illustrative examples with geometric interpretations to demonstrate the authenticity of the postulates. The motivation of this work is the fact that the set of nonunique fixed points may include a geometric figure like a circle, an ellipse, a disc, or an elliptic disc. Towards the end, we provide an application of Θ -contraction to chemical sciences.

Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.