Cona, Lale

Fractional calculus, which involves derivatives and integrals of non-integer order, is widely used in modeling real-world problems in science and engineering. This study focuses on solving fractional integro-differential equations using Picard's three-step iteration algorithm. We apply Picard's three-step iteration algorithm to approximate solutions and show that it converges strongly. The method is shown to be not only efficient in approximating solutions but also robust with respect to perturbations in the initial data and operators, demonstrating its data dependence. A numerical example is provided to illustrate the theoretical results and to confirm the applicability and reliability of the proposed approach.

Cona, Lale; Şimşek, Deniz

This article addresses the convergence of iteration sequences in Cesàro means for asymptotically nonexpansive mappings. Specifically, this study explores the behavior of Kirk iteration in the Cesàro means in the context of uniformly convex and reflexive Banach spaces equipped with uniformly Gâteaux differentiable norms. The focus is to determine the conditions under which the Kirk iteration sequence converges strongly or weakly to a fixed point. Finally, some examples are given in this article to demonstrate the advantages of the preferred iteration method and to verify the results obtained.

Cona, Lale; Tan, Gizem Güzel

Bu çalışmada, klasik analizde ve bulanık metrik uzaylarda tanımlı f ve ψ daralma dönüşüm sınıflarının sezgisel bulanık normlu uzaylar için yeni versiyonları tanımlanacaktır. Ayrıca, bu dönüşümlerin sezgisel bulanık normlu uzaylarda hangi şartlar altında yaklaşık sabit nokta özelliğini sağladığı gösterilecektir. Bulunan sonuç örneklerle desteklenecektir.

Cona, Lale; Sengül, Kadir

In this article, the solution of the second type of nonhomogeneous linear Fredholm integral equations is investigated using a three-step iteration algorithm. It has been shown that the sequences obtained from this algorithm converge to the solution of the mentioned equations. Morever, data dependency is obtained for the second type of nonhomogeneous linear Fredholm integral equations. This result is supported by an example.

Cona, Lale

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems.

Cona, Lale; Kaygusuz, Çiğdem

Bu makalede, ilk olarak toplanabilme teknikleri ve iterasyon yöntemleri araştırılmıştır. Ayrıca, bazı iterasyon yöntemleri için Cesàro anlamında toplanabilme tekniğine bağlı olarak ergodik teori üzerine yapılan çalışmalar incelenmiştir. Son olarak asimptotik genişlemeyen dönüşümler için Halpren iterasyonu ile Cesàro ortalamasının güçlü yakınsaklığı üzerine yapılan bir çalışma irdelenmiştir.

Cona, Lale; Bal, Esmahan

In this study, a sufficient condition for the existence and uniqueness of some fractional order Integral-Differential equations is obtained. Therefore, the fixed point method is used to solve the differential equation problem involving nonlinear degree integrals. In addition, the results found is supported by examples.

Cona, Lale; Şengül, Kadir

In this study, the solution of the second type of homogeneous nonlinear Fredholm integral equations is investigated using a three-step iteration algorithm. In other words, it has been shown that the sequences obtained from this algorithm converge to the solution of the mentioned equations. Also, data dependency is obtained for the second type of homogeneous nonlinear Fredholm integral equations and this result is supported by an example.

Cona, Lale; Alkan, Ünal Kemal

Bu çalışmasında Banach uzaylarda ki lineer sınırlı operatörler için s-sayı fonksiyonları üzerine bir araştırma yapılmıştır. Birinci bölümde s-sayı fonksiyonlarının gelişimi ve kullanıldığı yerler üzerine bilgi verilmiştir. İkinci bölümde bazı temel kavramlar hatırlatılmıştır. Üçüncü bölümde ise bazı önemli s-sayıları örnekleri verilmiştir. Ayrıca farklı operatörler için s-sayıları arasında ki bağıntılara yer verilmiştir. Böylece bir bütün olarak Banach uzaylarda s-sayılarının aksiyomatik teorisi sunulmuştur.

Cona, Lale

In this work, two problems are investigated. In general. Weyl-type inequalities of operators in complex reflexive Banach spaces are discussed. Fir st, w'e obtained the Weyl-type inequalities using arbitrary multiplicative surjective and injective s-numbers that are dual of each other. Second, w'e introduced the Weyl-type inequalities by multiplicative injective and surjective s- numbers under certain conditions for S and S' operators hi complex reflexive Banach space. So. new Weyl-type inequalities are investigated for both dual s-number sequences and dual operators.

Ismailov, Zameddin I.; Cona, Lale; Çevik, Elif Otkun; Guler, Bahadir O.; Ashyralyev, A; Malkowsky, E

In this work, a connection between Weyl numbers of the infinite diagonal matrix with linear bounded operator elements in the direct sum of Banach spaces and its coordinate operators has been investigated.