Kısmi Metrik Uzaylarda İntegral Tip Büzülme İçin Sabit Nokta Teoremleri

Year 2018, , 410 - 417, 31.07.2018

Vildan Ozturk

https://doi.org/10.17714/gumusfenbil.395598

Abstract

Bu
çalışmada kısmi metrik uzaylarda, uzaklığı değiştiren fonksiyonlar aracılığıyla
(E.A)-özelliğini sağlayan dönüşümler için integral tipli büzülme tanımlanmış ve
bu tipteki büzülmeyi sağlayan dört dönüşüm için ortak sabit nokta teoremi ispatlanmıştır.

Keywords

İntegral tipli büzülme, Kısmi metrik, Sabit nokta

Fixed Point Theorems for Integral Type Contraction in Partial Metric Spaces

Abstract

In this work, integral type contraction by altering distance
functions for mappings satisfying (E.A)-property was introduced and common
fixed point theorems for four mappings satisfying this type contraction was
proved.

Keywords

Integral type contraction, Partial metric, Fixed point

References

• Aamri, M. ve El-Moutawakil, D., 2002. Some new common fixed point theorems under strict contractive conditions. Journal Of Mathematical Analysis And Applications, 270, 181-188.
• Abdeljawad, T., 2011. Fixed points for generalized weakly contractive mappings in partial metric spaces. Mathematical and Computer Modelling, 54, 2923-2927.
• Altun, I., Sola, F. ve Simsek, H., 2010. Generalized contractions on partial metric spaces. Topology And Its Applications, 157, 2778-2785.
• Babu, G.V.R., Lalitha, B. ve Sandhya, M.L., 2007. Common fixed point theorems involving two generalized altering distance functions in four variables. Prooceding Of The Jangjeon Mathematical Society, 10 (1), 83-93.
• Banach, S., 1922. Sur les oprations dans les ensembles abstraits et leur applications aux equations integrales. Fundemental Mathematics, 3, 133-181.
• Branciari, A., 2002. A fixed point theorem for mappings satisfying a general contractive condition of integral type. International Journal of Mathematics and Mathematical Sciences, 29 (9), 531-536.
• Dutta, P.N. ve Binayak, S.C., 2008. A generalisations of contraction principle in metric spaces, Fixed Point Theory and Appl., 2008, Article ID 406368.
• Jungck, G., 1986. Compatible mappings and common fixed points. Int. J. Math. Sci., 9, 771-779.
• Kadelburg, Z., Nashine, H.K. ve Radenovic, S. 2013. Fixed point results under various contractive conditions in partial metric spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 107 (2), 241-256.
• Karapinar, E., 2011. Generalizations of Caristi Kirk’s theorem on partial metric spaces, Fixed Point Theory and Applications, 2011, Article ID 4.
• Matthews, S.G., 1992. Partial Metric Topology, Research Report 212, Department Of Computer Science University Of Warwick.
• Matthews, S.G., 1994. Partial Metric topology in Proceedings of the 8th Summer Conference at Queens College,S. Andima, Ed., 728 of Papers on General Topology and Applications, Annals of the New YorkAcademy of Sciences 183-197.
• Naidu, S.V.R., 2003. Some fixed point theorems in metric spaces by altering distances. Czechoslovak Mathematical Journal, 53 (1), 205-212.
• Nazir, T. ve Abbas, M., 2014. Common fixed points of two pairs of mappings satisfying (E.A)-property in partial metric spaces. J. Inequal. Appl. 2014, Article ID 23.
• Rhoades, B.E., 2001. Some theorems on weakly contractive maps. Nonlinear Analysis: Theory, Methods and Applications, 47 (4), 2683-2693.
• Turkoglu, D. ve Ozturk, V., 2012. Common fixed point results for four mappings on partial metric spaces. Abstract And Applied Analysis, Article ID 190862.
• Valero, O., 2005. On Banach fixed point theorems for partial metric spaces. Applied General Topology, 6 (2), 229-240.