A New Approach to Fuzzy Differential Equations Using Weakly-Compatible Self-Mappings in Fuzzy Metric Spaces

The key objective of this research article includes the study of some rational type coincidence point and deriving common fixed point (CFP) results for rational type weakly-compatible three self-mappings in fuzzy metric (FM) space. The “triangular property of FM” is used as a fundamental tool. Moreover, some unique coincidence points and CFP theorems were presented for three self-mappings in an FM space under the conditions of rational type weakly-compatible fuzzy-contraction. In addition, some suitable examples are also given. Furthermore, an application of fuzzy differential equations is provided in the aid of the proposed work. Hence, the innovative direction of rational type weakly-compatible fuzzy-contraction with the application of fuzzy differential equations in FM space will certainly play a vital role in the related fields. It has the potential to be extended in any direction with different types of weakly-compatible fuzzy-contraction conditions for self-mappings with different types of differential equations.

Some Theorems on Integral and Rational Type Contractive Conditions in Dislocated Metric Space

In this article, we establish some coincidence points and common fixed point results on integral and rational type contractive conditions using E.A. and common limit range (CLR) properties in dislocated metric space.

Inceptions

The beginning is both internal and external to the text it initiates, and that non-coincidence points to the text’s vexed relation with its outside. Hence the non-trivial self-reflexivity of any textual beginning, which must bear witness to the self-grounding quality of the literary work—its inability either to comprise its inception or to externalize it in an authorizing exteriority. In a different but related way does the fact that they must render our lives and our desires opaque to us; what Freud called “latency” marks not only sexuality but human thought with a self-division shaped by asynchronicity. From Henry James’s New York Edition prefaces to George Eliot’s epigraphs, from Ovid’s play with meter to Charles Dickens’s thematizing of the ex nihilo emergence of character, from Wallace Stevens’s abstract consideration of poetic origins to James Baldwin, Carson McCullers, and Eudora Welty’s descriptions of queer childhood, writers repeatedly confront the problem of inception. Most explicitly for James, for whom revision, a striving to keep the work perpetually at the border of its emergence, was a fundamentally ethical practice, attention to inception is a commitment to human freedom; a similar commitment is legible in all the writers examined here. To experience this vibrancy, the sense that the work might have been, might still yet be, otherwise, it suffices, James reminds us, to reread it. Inceptions traces an ethics of reading, that follows from perceiving, in the ostensibly finished forms of lives and texts, the potentiality inherent in their having started forth.

On Global Solvability of Nonlinear Equations with Parameters

We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.

Coincidence points in θ - metric spaceS

In this paper, inspired by the concept of metric space, two fixed point theorems for α−set-valued mapping T:₳ → CB(₳), h θ (Tp,Tq) ≤ α(dθ(p,q)) dθ(p,q), where α: (0,∞) → (0, 1] such that α(r) < 1, ∀ t ∈ [0,∞) ) are given in complete θ −metric and then extended for two mappings with R-weakly commuting property to obtain a common coincidence point.

Generalized cyclic contractions and coincidence points involving a control function on partial metric spaces

PurposeIn this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.Design/methodology/approachTheoretical method.FindingsWe establish some coincidence points and common fixed point results in partial metric spaces.Originality/valueResults of this study are new and interesting.