Some remarks on bv(s)-metric spaces and fixed point results with an application

We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations.

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Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

Journal of Function Spaces ◽

10.1155/2021/9982217 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Santosh Kumar

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Volterra Integral Equations ◽

Discontinuous Mappings ◽

Contractive Maps ◽

Uniqueness Of A Solution ◽

Type Contraction

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

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Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽

10.3390/math9182267 ◽

2021 ◽

Vol 9 (18) ◽

pp. 2267

Author(s):

Hasanen A. Hammad ◽

Manuel De la De la Sen

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Control Function ◽

Cone Metric Spaces ◽

Tripled Fixed Point ◽

Contractive Type ◽

Theoretical Results ◽

Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

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Solving a Class of Integral Equations via Contractive Mapping with Rational Type

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v13i4.3831 ◽

2020 ◽

Vol 13 (4) ◽

pp. 995-1015

Author(s):

Abdullah Abdullah ◽

Muhammad Sarwar ◽

Zead Mustafa ◽

Mohammed M.M. Jaradat

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Coupled Fixed Point ◽

Contractive Mapping ◽

Coupled Fixed Point Theorem ◽

Set Up ◽

Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

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Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces

Arab Journal of Mathematical Sciences ◽

10.1108/ajms-10-2020-0098 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Godwin Amechi Okeke ◽

Daniel Francis

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Fredholm Integral Equations ◽

Fredholm Type ◽

Content Type ◽

Special Cases ◽

Type Integral ◽

Social Applications

PurposeThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.Research limitations/implicationsThe results are theoretical and analytical.Practical implicationsThe results were applied to solving nonlinear integral equations.Social implicationsThe results has several social applications.Originality/valueThe results of this paper are new.

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On a class of nonlinear Volterra-Fredholm q-integral equations

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0155-7 ◽

2014 ◽

Vol 17 (1) ◽

Cited By ~ 4

Author(s):

Zeinab Mansour

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Integral Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Fredholm Integral Equations ◽

Banach Fixed Point Theorem ◽

Continuous Solutions ◽

Projective Metric ◽

Uniqueness Criteria

AbstractIn this paper we investigate the existence and uniqueness of positive continuous solutions for a q-analogue of Volterra and Fredholm integral equations of first and second kinds. We derive the results by using three fixed point theorems introduced by Bushell in [7, 8]. Bushell derived his theorems by using the Cayley-Hilbert projective metric and Banach fixed point theorem. We also include some uniqueness criteria for the solutions of certain nonlinear q-integral equations provided that the solution exists in certain function spaces.

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The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽

10.3390/math9010029 ◽

2020 ◽

Vol 9 (1) ◽

pp. 29

Author(s):

Maria Dobriţoiu

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Integral Equations ◽

Volterra Integral Equation ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Nonlinear Integral Equations ◽

Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

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Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽

10.2298/fil1410047n ◽

2014 ◽

Vol 28 (10) ◽

pp. 2047-2057 ◽

Cited By ~ 10

Author(s):

Kumar Nashine ◽

Zoran Kadelburg

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Points ◽

Integral Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Existence Problem ◽

Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

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C*-Algebra Valued Partial b-Metric Spaces and Fixed Point Results with an Application

Mathematics ◽

10.3390/math8081381 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1381

Author(s):

Nabil Mlaiki ◽

Mohammad Asim ◽

Mohammad Imdad

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Fredholm Integral Equations ◽

Partial Metric ◽

C Algebra ◽

Partial Metric Spaces ◽

Uniqueness Of A Solution

In this paper, we enlarge the class of C*-algebra valued partial metric spaces as well as the class of C*-algebra valued b-metric spaces by introducing the class of C*-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations.

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Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

Advances in Difference Equations ◽

10.1186/s13662-021-03255-6 ◽

2021 ◽

Vol 2021 (1) ◽

Cited By ~ 2

Author(s):

Hasanen A. Hammad ◽

Hassen Aydi ◽

Nabil Mlaiki

Keyword(s):

Fixed Point ◽

Integral Equations ◽

Metric Spaces ◽

Integral Operators ◽

Volterra Integral Equations ◽

Fractional Integrals ◽

Uniqueness Of Solutions ◽

Mild Conditions ◽

Contractive Type ◽

Theoretical Results

AbstractIn this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, $\eta _{\gimel }^{\nu }$ η ℷ ν -metric spaces) are obtained. Moreover, some related consequences dealing with a common fixed point concept and nontrivial examples to support our results are presented. Ultimately, we use the theoretical results to discuss the existence and uniqueness of solutions of 2D Volterra integral equations, Riemann–Liouville integrals and Atangana–Baleanu integral operators are given.

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Modified F-contractions via α-admissible mappings and application to integral equations

Filomat ◽

10.2298/fil1705141a ◽

2017 ◽

Vol 31 (5) ◽

pp. 1141-1148 ◽

Cited By ~ 17

Author(s):

Hassen Aydi ◽

Erdal Karapinar ◽

Habib Yazidi

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Integral Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Complete Metric Spaces

In this paper, we introduce the concept of a modified F-contraction via ?-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.

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