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Article Citation - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.Article Citation - WoS: 13Citation - Scopus: 14The Existence of Optimal Approximate Solution Theorems for Generalized Α-Proximal Contraction Non-Self Mappings and Applications(Springer international Publishing Ag, 2013) Karapinar, Erdal; Sintunavarat, WutipholIn this paper, we investigate the sufficient conditions to find a best proximity point for a certain class of non-self mappings. It is well known that optimization problems can be transformed to the problems of the existence of a best proximity point. Hence, improvement in the best proximity point theory implicitly develops the theory of optimization. Our presented results generalize, extent and improve various well-known results on the topic in the literature. In particular, we consider some applications of our results to the best proximity point theorems on a class of metric spaces endowed with an arbitrary binary relation which involves the partially ordered metric spaces.Article Citation - WoS: 13Citation - Scopus: 18On the existence of fixed points that belong to the zero set of a certain function(Springer international Publishing Ag, 2015) Karapinar, Erdal; O'Regan, Donal; Samet, BessemLet T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem.Book Part Citation - WoS: 15Citation - Scopus: 15Comparison of Hematopoietic and Spermatogonial Stem Cell Niches From the Regenerative Medicine Aspect(Springer international Publishing Ag, 2018) Kose, Sevil; Yersal, Nilgun; Onen, Selin; Korkusuz, PetekRecent advances require a dual evaluation of germ and somatic stem cell niches with a regenerative medicine perspective. For a better point of view of the niche concept, it is needed to compare the microenvironments of those niches in respect to several components. The cellular environment of spermatogonial stem cells' niche consists of Sertoli cells, Leydig cells, vascular endothelial cells, epididymal fat cells, peritubular myoid cells while hematopoietic stem cells have mesenchymal stem cells, osteoblasts, osteoclasts, megacaryocytes, macrophages, vascular endothelial cells, pericytes and adipocytes in their microenvironment. Not only those cells', but also the effect of the other factors such as hormones, growth factors, chemokines, cytokines, extracellular matrix components, biomechanical forces (like shear stress, tension or compression) and physical environmental elements such as temperature, oxygen level and pH will be clarified during the chapter. Because it is known that the microenvironment has an important role in the stem cell homeostasis and disease conditions, it is crucial to understand the details of the microenvironment and to be able to compare the niche concepts of the different types of stem cells from each other, for the regenerative interventions. Indeed, the purpose of this chapter is to point out the usage of niche engineering within the further studies in the regenerative medicine field. Decellularized, synthetic or non-synthetic scaffolds may help to mimic the stem cell niche. However, the shared or different characteristics of germ and somatic stem cell microenvironments are necessary to constitute a proper niche model. When considered from this aspect, it is possible to produce some strategies on the personalized medicine by using those artificial models of stem cell microenvironment.Article Citation - WoS: 28Citation - Scopus: 33Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in g-metric Spaces(Springer international Publishing Ag, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; de la Sen, ManuelIn this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.Article Citation - WoS: 60Citation - Scopus: 72Remarks on some coupled fixed point theorems in G-metric spaces(Springer international Publishing Ag, 2013) Agarwal, Ravi P.; Karapinar, ErdalIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.Article Citation - WoS: 3Citation - Scopus: 6Fixed Points of Α-Admissible Meir-Keeler Contraction Mappings on Quasi-Metric Spaces(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Gulyaz, Selma; Erhan, Inci M.We introduce alpha-admissible Meir-Keller and generalized alpha-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.Article Citation - WoS: 45Citation - Scopus: 47(α, ψ, ξ)-contractive multivalued mappings(Springer international Publishing Ag, 2014) Ali, Muhammad Usman; Kamran, Tayyab; Karapinar, ErdalIn this paper, we introduce the notion of (alpha, psi, xi)-contractive multivalued mappings to generalize and extend the notion of alpha-psi-contractive mappings to closed valued multifunctions. We investigate the existence of fixed points for such mappings. We also construct an example to show that our result is more general than the results of alpha-psi-contractive closed valued multifunctions.Article Citation - WoS: 29Citation - Scopus: 42Mixed g-monotone Property and Quadruple Fixed Point Theorems in Partially Ordered Metric Spaces(Springer international Publishing Ag, 2012) Mustafa, Zead; Aydi, Hassen; Karapinar, ErdalIn this manuscript, we prove some quadruple coincidence and common fixed point theorems for F : X-4 -> X and g : X -> X satisfying generalized contractions in partially ordered metric spaces. Our results unify, generalize and complement various known results from the current literature. Also, an application to matrix equations is given.Article Citation - WoS: 15Citation - Scopus: 15A Note on 'ψ-geraghty Type Contractions'(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemVery recently, the notion of a psi-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012: 74, 2012). In this short note, we realize that the main result via psi-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way.
