Integral type contractions of soft set-valued maps with application to neutral differential equations

Shagari, Mohammed Shehu; Azam, Akbar

doi:10.3934/math.2020023

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…Afterward, Heilpern [15] presented the theory of fuzzy mapping (FM) by utilizing the idea of FSs and furnished an FP Theorem for fuzzy contraction maps which is considered as a fuzzy version of Nadler's [16] and Banach's [17] FP Theorems. After that, a wide number of researchers worked for the existence of FPs for FMs, see, for example, [18,19]. Later, in 1967, the concept of £-FSs was furnished by Goguen [20], which is an intriguing generalization of FSs because it replaced the interval [0, 1] by a complete distributive lattice.…”

Section: Introductionmentioning

confidence: 99%

A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £-Fuzzy Fixed Points with Application

Rashid,

Azam,

Dar

et al. 2023

Mathematics

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Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy Z-contraction in the perspective of £-fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining £-fuzzy fixed points for this contraction have been established. In addition, the hypotheses of its main result are endorsed by some nontrivial supportive examples featuring graphical illustrations. Consequently, the concept of graphical extended ♭-metric spaces is introduced and a £-fuzzy fixed point result in the context of newly defined space is derived. Illustrative examples, incorporating relevant graphs, are provided with the support of a computer simulation to validate the established results, enhancing the understanding of the underlying notions and investigations. The concepts presented here not only considerably improve, enrich, and extend a number of well-known pre-existing fixed-point results but also assemble and merge several ones in the corresponding domain.

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Section: Introductionmentioning

confidence: 99%

A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £-Fuzzy Fixed Points with Application

Rashid,

Azam,

Dar

et al. 2023

Mathematics

Self Cite

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“…Since then, research works in soft sets theory and its applications in various fields have been progressing rapidly because this theory is free from the many difficulties that have troubled the usual theoretical approaches. This is how research related to soft sets has been carried out in several directions among which we can mention the following: information systems, decision making, nonlinear neutral differential equations and algebraic structures, fuzzy sets, and rough sets, as we can see in the papers [12][13][14][15][16]. In particular, regarding mathematical analysis and its applications, the concepts and results of soft real sets, soft real numbers, soft complex sets, soft complex numbers, soft linear spaces, soft metric spaces, soft normed spaces, soft inner product, soft Hilbert spaces, soft linear operator, soft linear functional, soft Banach algebra, soft topology, etc., have originated (see [11,[17][18][19][20][21][22][23][24][25][26]).…”

Section: Introductionmentioning

confidence: 99%

Soft Frames in Soft Hilbert Spaces

2021

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In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.

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Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

Alansari

Shagari

Azam³

2022

Mathematica Slovaca

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In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b-metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

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Integral type contractions of soft set-valued maps with application to neutral differential equations

Cited by 6 publications

References 21 publications

A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £-Fuzzy Fixed Points with Application

A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £-Fuzzy Fixed Points with Application

Soft Frames in Soft Hilbert Spaces

Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

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