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Öğe Common fixed point of g-approximative multivalued mapping in ordered partial metric space(Springer International Publishing Ag, 2013) Erduran, AliIn this paper, we introduce g-approximative multivalued mappings to a partial metric space. Based on this definition, we give some new definitions. Further, common fixed point results for g-approximative multivalued mappings satisfying generalized contractive conditions are obtained in the setup of ordered partial metric spaces.Öğe Common fixed point of g-approximative multivalued mapping in partially ordered metric space(Univ Nis, Fac Sci Math, 2013) Abbas, Mujahid; Erduran, AliIn this paper, we introduce g-approximative multivalued mappings. Based on this definition, we gave some new definitions. Further, common fixed point results for g-approximative multivalued mappings satisfying generalized contractive conditions are obtained in the setup of ordered metric spaces. Our results generalize Theorems 2.6-2.9 given in ([1]).Öğe Fixed point results for single valued and set valued P-contractions and application to second order boundary value problems(NORTH UNIV BAIA MARE, 2020) Altun, Ishak; Hancer, Hatice Aslan; Erduran, AliIn this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem.Öğe A fixed point theorem for (φ,L)-weak contraction mappings on a partial metric space(Int Scientific Research Publications, 2014) Erduran, Ali; Kadelburg, Z.; Nashine, H. K.; Vetro, C.In this paper, we explore (phi, L)-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature. (C)2014 All rights reserved.Öğe Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces(Springer International Publishing Ag, 2011) Altun, İshak; Erduran, AliMatthews (1994) introduced a new distance p on a nonempty set X, which is called partial metric. If (X,p) is a partial metric space, then p(x,x) may not be zero for x is an element of X. In the present paper, we give some fixed point results on these interesting spaces.Öğe Fixed point theory for Suzuki type (θ,L)-weak multivalued operators(House Book Science-Casa Cartii Stiinta, 2015) Erduran, Ali; Abbas, MujahidExistence of a fixed point of Suzuki type (theta, L)- weak multivalued operator is obtained. As an application, we obtain homotopy and data dependence results for Suzuki type contractive multivalued operator. Our results complement and extend some very recent comparable results in the existing literature.Öğe Generalized Meir-Keeler type n-tupled fixed point theorems in ordered partial metric spaces(Springer International Publishing Ag, 2014) Imdad, Mohammad; Sharma, Anupam; Erduran, AliIn this paper, we prove n-tupled fixed point theorems (for even n) for mappings satisfying Meir-Keeler type contractive condition besides enjoying mixed monotone property in ordered partial metric spaces. As applications, some results of integral type are also derived. Our results generalize the corresponding results of Erduran and Imdad (J. Nonlinear Anal. Appl. 2012: jnaa-00169, 2012).Öğe Metrik tamlığı karakterize eden bazı sabit nokta teoremleri(Kırıkkale Üniversitesi, 2012) Erduran, Ali; Altun, İshakBu tez çalışmasında, Banach büzülme prensibinin metrik uzayın tamlığını karakterize eden bir genellemesi verildi. Ardından, Kannan, Chatterjea gibi bazı genelleştirmeleri incelendi. Daha sonra, Suziki sabit nokta teoreminin kapalı bağıntı yardımıyla bir genellemesi verildi.Öğe Nonself P-contractions on convex metric spaces and their fixed points(Springernature, 2022) Altun, Ishak; Hancer, Hatice Aslan; Erduran, AliIn this paper, we present some new fixed point results for single-valued nonself mappings from a closed subset K of a metrically convex metric space M into M. Here we consider recent approaches for contractive condition named as P-contraction. We provide some examples to support our results. Then by taking into account the compactness of the subset K, we consider a strict version of P-contraction without contractive constant and so we present a new result. Finally, we give the nonself version of the famous Edelstein fixed point theorem as corollary.Öğe Preši?-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations(Vilnius University Press, 2023) Altun, Ishak; Gençtürk, İlker; Erduran, AliIn this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Preši?-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example. © 2023 The Author(s).Öğe Presic-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations(Vilnius Univ, Inst Mathematics & Informatics, 2023) Altun, Ishak; Gencturk, Ilker; Erduran, AliIn this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Presic-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.Öğe RAKOTCH TYPE EXTENSION OF DARBO'S FIXED POINT THEOREM AND AN APPLICATION(Univ Politehnica Bucharest, Sci Bull, 2024) Gencturk, Ilker; Erduran, Ali; Altun, IshakIn this paper, we present a new extension of Darbo's fixed point theorem inspired by Rakotch's contraction. We also provide the alternative version of Leray-Schauder type of our new result. In order to demonstrate the applicability of our theoretical result, we present an existence theorem based on a functional equation. Finally, we provide an illustration of our existence theorem.Öğe RAKOTCH TYPE EXTENSION OF DARBO’S FIXED POINT THEOREM AND AN APPLICATION(Politechnica University of Bucharest, 2024) Gençtürk, İlker; Erduran, Ali; Altun, IshakIn this paper, we present a new extension of Darbo’s fixed point theorem inspired by Rakotch’s contraction. We also provide the alternative version of Leray-Schauder type of our new result. In order to demonstrate the applicability of our theoretical result, we present an existence theorem based on a functional equation. Finally, we provide an illustration of our existence theorem. © 2024, Politechnica University of Bucharest. All rights reserved.Öğe Some fixed point theorems for singlevalued and multivalued P- contraction mappings(Kırıkkale Üniversitesi, 2022) Erduran, Ali; Altun, İshakBu tez çalışması üç temel kısımdan oluşmaktadır, birinci kısımda metrik sabit nokta teori alanı ile ilgili genel bilgiler verildikten sonra çalışmalarımızda temel büzülme tipi olan P- büzülme, ayrıca sabit noktada bilinen ve çalışmalarımızda temel olarak kullandığımız teoremler verildi. İkinci kısımda metrik uzayda tek değerli ve küme değerli P- büzülme dönüşümler için sabit nokta teoremi ve sonuçları, ayrıca konveks metrik uzayda nonself dönüşümler için sabit nokta teoremi ve sonuçları, en son olarak da yeni bir uzay olarak çalışılan F-metrik ile ilgili temel tanım ve teoremler verildikten sonra P- büzülme üzerine sabit nokta teoremi sonuçları verildi. Son kısım tartışma ve sonuç kısmı olup tez çalışmamız ile ilgili son değerlendirmeler yapıldı.Öğe Two fixed point results on F-metric spaces(De Gruyter Open Ltd, 2022) Altun, Ishak; Erduran, AliThis paper presents two fixed point results for both single valued and multivalued mappings on F-metric spaces, which is introduced by Jleli and Samet [1]. First, we consider the concept of P-contraction for single valued mappings. Then using the Feng-Liu's technique, we present a fixed point result for F-closed set valued mappings on F-metric spaces. © 2022 Ishak Altun et al., published by De Gruyter.
