Fixed Point Results for α-Admissible Multivalued F-Contractions

Altun, Ishak/0000-0002-7967-0554WOS: 000390602900015In this study, we give some fixed point results for multivalued mappings using Pompeiu-Hausdorff distance on complete metric space. For this, we consider the alpha-admissibility of multivalued mappings. Our results are real generalizations of Mizoguchi-Takahashi fixed point theorem. We also provide an example showing this fact. Finally, we obtain some ordered fixed point results for multivalued mappings

Weak partial metric spaces and some fixed point results

[EN] The concept of partial metric p on a nonempty set X was introduced by Matthews. One of the most interesting properties of a partial metric is that p(x, x) may not be zero for x e X. Also, each partial metric p on a nonempty set X generates a T0 topology on X. By omitting the small self-distance axiom of partial metric, Heckmann defined the weak partial metric space. In the present paper, we give some fixed point results on weak partial metric spaces.Altun, I.; Durmaz, G. (2012). Weak partial metric spaces and some fixed point results. Applied General Topology. 13(2):179-191. doi:10.4995/agt.2012.1628SWORD17919113

Sıralı koni metrik uzaylarda sabit nokta teoremleri

Tez (Yüksek Lisans) -- Kırıkkale ÜniversitesiKaynakça var.78403

Some fixed point theorems on weak partial metric space

YÖK Tez ID: 418460Bu tez çalışmasının giriş bölümünde, gündelik yaşam, matematik ve sabit nokta teori arasındaki ilişki hakkında bir bilgi verilmiştir. Ardından, materyal ve yöntem bölümünde, tez içerisinde yararlanılacak kısmi metrik uzay kavramı ve ilgili temel tanımlar ve teoremler verilmiştir. Daha sonra tezin orijinal kısmını oluşturan üçüncü bölüm iki kısımdan oluşmaktadır. İlk kısımda, zayıf kısmi metrik kavramı ile ilgili tanım verilerek, bu kavram örneklerle incelenmiştir. Bu tanımdan yararlanılarak önemli sabit nokta teoremleri olan Banach, Kannan, Chatterjea, Hardy-Rogers ve Berinde sabit nokta teoremleri ve bunların genelleştirmeleri zayıf kısmi metrik uzayda verilmiştir. İkinci kısımda, lineer olmayan dönüşümler için sabit nokta teoremleri verilmiştir. Ayrıca bu sonuçların uygulamalarından da bahsedilmiştir. Elde edilen sonuçların literatürde daha önce verilen sabit nokta sonuçlarının genelleştirilmesi olduğu gösterilmiş ve örneklerle desteklenmiştir. Son bölüm olan tartışma ve sonuç bölümünde, elde edilen sonuçların önemi ve bunların literatürdeki bazı sabit nokta teoremlerinin genelleştirmeleri olduğu vurgulanmıştır.In the introduction of this thesis, the information about the relationship between daily life, mathematics and fixed point theory is given. Then, in the material and method section, the basic definitions and theorems related to the concept of partial metric space to be utilized in the thesis are given. Later, the third section forming the original section of the thesis consists of two parts. In the first part, the concept of a weak partial metric is given and the examples of the concept have been examined. By utilizing the definition, Banach, Kannan, Chatterjea, Hardy-Rogers and Berinde fixed point theorems which are important for fixed point theory and their generalizations are given in the weak partial metric space. In the second part, fixed point theorems for non-linear mappings are given on metric space. It has also been mentioned about the application of the results. The obtained results are the generalization of fixed point results given previously in the literature and these results are supported with examples. In the last section including discussion and conclusions, it is emphasized that the importance of the obtained results and generalizations of some fixed point theorems in their literature

Zayıf kısmi metrik uzayda bazı sabit nokta teoremleri

Tez (Doktora) -- Kırıkkale Üniversitesi100188

Fixed point teorems on ordered cone metric spaces

YÖK Tez ID: 258944Bu tez çalışmasında sıralı koni metrik uzay üzerinde bazı sabit nokta teoremleri incelenmiştir. İlk olarak sabit nokta teorisi ile ilgili ön bilgiler, bazı temel tanım ve teoremler verilmiştir. İkinci olarak sıralı metrik uzaylarda sabit nokta teorisi incelenip normal metrik uzayla arasındaki farklar belirtilmiştir. Daha sonra son yıllarda tanımlanan koni metrik uzay kavramı verilerek bununla ilgili temel tanım, teoremler ve bu uzayda sabit nokta teorisi incelenmiştir. Son olarak bu tez çalışmasının orijinal kısmını oluşturan sıralı koni metrik uzaylarda sabit nokta teoremleri incelenerek koni metrik uzaylardaki teoremleri ile arasındaki farklar incelenmiştir.In this study, some fixed points theorems on ordered cone metric space have been analyzed. Initially, background information, some essential definitions and theorems were given about fixed point theorem. Secondly, fixed point theorem on ordered cone metric space was investigated, and its differences from usual metric space were determined. After that, recently identified cone metric space term was given, and basic definition, theorems, and fixed point theorem were investigated for this space. Finally, fixed point theorems on ordered cone metric spaces constituting the original part of this study were analyzed, and differences between these theorems and theorems on cone metric spaces are investigated

A NEW PERSPECTIVE FOR MULTIVALUED WEAKLY PICARD OPERATORS

Altun, Ishak/0000-0002-7967-0554WOS: 000403745800018This research contains some recent developments about multivalued weakly Picard operators on complete metric spaces. In addition, taking into account both multivalued theta-contraction and almost contraction on complete metric spaces, we present a new perspective for multivalued weakly Picard operators. Finally, we give a nontrivial example showing that the investigation of this paper is significant

On Nonlinear Set-Valued theta-Contractions

WOS: 000526822700023In this paper, we introduce and study new fixed point results for nonlinear set-valued theta-contractions. Our results are based on a new approach, which is called set-valued theta-contraction and they extend and generalize many fixed point theorems in the literature

A Fixed Point Theorem for New Type Contractions on Weak Partial Metric Spaces

Altun, Ishak/0000-0002-7967-0554WOS: 000212590700013Recently, Karapinar and Romaguera (Filomat 27: 1305-1314, 2013) have introduced a new type contraction on partial metric spaces, and they have obtained a nonunique fixed point result. Then Romaguera (Math. Sci. Appl. E-Notes 1: 1-8, 2013) used this contraction to obtain some multivalued fixed point results on partial metric spaces. In the present work, we give a fixed point result on weak partial metric spaces using this new idea.Scientific and Technological Research Council of Turkey (TUBITAK) TBAGTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [212T212]This paper is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) TBAG project no. 212T212. The authors are grateful to the referees for their suggestions that contributed to improve the paper

Some fixed point results on weak partial metric spaces

Altun, Ishak/0000-0002-7967-0554WOS: 000322027700011The concept of partial metric p on a nonempty set X was introduced by Matthews [13] and it was slightly modified by Heckmann [11] as weak partial metric. In [12], the authors studied fixed point result of new extension of Banach's contraction principle to partial metric space and give some generalized versions of the fixed point theorem of Matthews. In the present paper, we extend and generalize the previous results to weak partial metric spaces