Yazar "Cakan, Umit" seçeneğine göre listele

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    AN APPLICATION OF DARBO FIXED- POINT THEOREM TO A CLASS OF FUNCTIONAL INTEGRAL EQUATIONS
    (Taylor & Francis Inc, 2015) Cakan, Umit; Ozdemir, Ismet
    In this article, using Darbo's fixed-point theorem associated with the measure of noncompactness, we prove a theorem on the existence of the solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. Our existence results include several existence results obtained earlier by Maleknejad et al. [7] and ozdemir et al. [8] as special cases under some weaker conditions. We give also some examples which show that our results are applicable.
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    Applications of Measure of Noncompactness and Darbo's Fixed Point Theorem to Nonlinear Integral Equations in Banach Spaces
    (Taylor & Francis Inc, 2017) Cakan, Umit; Ozdemir, Ismet
    We prove a theorem on the existence of solutions of some nonlinear functional integral equations in the Banach algebra of continuous functions on the interval [0,a]. Then we consider a nonlinear integral equation of fractional order and give some sufficient conditions for existence of solutions of this equation. We use fixed point theorems associated with the measure of noncompactness as the main tool. Our existence results include several results obtained in previous studies. Finally we present some examples which show that our results are applicable.
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    ASYMPTOTIC STABILITY OF SOLUTIONS FOR A CLASS OF NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS OF FRACTIONAL ORDER
    (Akademiai Kiado Rt, 2016) Cakan, Umit; Ozdemir, Ismet
    In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [ 0,infinity). We also give some examples satisfying the conditions our existence theorem.
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    Existence of nondecreasing solutions of some nonlinear integral equations of fractional order
    (Int Scientific Research Publications, 2015) Cakan, Umit; Ozdemir, Ismet
    The purpose of this paper is to examine the class of functional integral equations of fractional order in the space of continuous functions on interval [0, a]. Using Darbo's fixed point theorem associated with the measure of noncompactness, we present sufficient conditions for existence of nondecreasing solutions of some functional integral equations of fractional order. These existence results include several obtained from previous studies. Finally, we establish some examples to show that our results are applicable. (C) 2015 All rights reserved.
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    EXISTENCE OF SOLUTIONS FOR 2D NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACE
    (Rocky Mt Math Consortium, 2023) Saini, Parul; Cakan, Umit; Deep, Amar
    We study the existence of solutions for 2D fractional Volterra integral equations, using Petryshyn's fixed-point theorem and measures of noncompactness in the Banach space C([0, a] x [0, b], R). Our results generalize results gained from earlier studies under some weaker conditions. We present some examples applying our results.
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    On the Existence of the Solutions for Some Nonlinear Volterra Integral Equations
    (Hindawi Publishing Corporation, 2013) Ozdemir, Ismet; Cakan, Umit; Ilhan, Bekir
    We present a theorem which gives sufficient conditions for existence of at least one solution for some nonlinear functional integral equations in the space of continuous functions on the interval [0, a]. To do this, we will use Darbo's fixed-point theorem associated with the measure of noncompactness. We give also an example satisfying the conditions of our main theorem but not satisfying the conditions described by Maleknejad et al. (2009).
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    A Result on Solvability of Some Fractional Integro-differential Equations in Abstract Spaces
    (Springer Singapore Pte Ltd, 2020) Cakan, Umit
    This paper concerns with a class of fractional integro-differential equations in the space of continuous functions which defined on interval [0, a] and take values in a Banach space E. Using a generalized Darbo fixed-point theorem associated with measure of noncompactness, the existence of solutions has been established. Also an example which shows that the main result is applicable is given.
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    SOLVABILITY FOR FRACTIONAL INTEGRAL EQUATIONS VIA PETRYSHYN'S FIXED-POINT THEOREM
    (Rocky Mt Math Consortium, 2023) Deep, Amar; Saini, Deepika; Singh, Hitesh Kumar; Cakan, Umit
    We examine the solvability of fractional integral equations using the techniques of measure of noncompactness and the Petryshyn's fixed-point theorem in Banach space concerning the Riemann-Liouville integral operator. The results obtained in this paper cover some earlier results obtained by numerous authors under weaker conditions. In the end, two applications are given to illustrate the major result.
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    THE SOLVABILITY OF SOME NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS
    (Akademiai Kiado Rt, 2016) Ozdemir, Ismet; Cakan, Umit
    In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable.