Some properties of short exact sequences of locally convex Riesz spaces

summary:We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces

Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

In this paper we introduce generalized cyclic contractions in G-metric spaces and establish some fixed point theorems. The presented theorems extend and unify various known fixed point results. Examples are given in the support of these results. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is given

Common fixed point theorems via common limit range property in symmetric spaces under generalized Phi-contractions

The aim of this paper is to use common limit range property for a quadruple of non-self mappings for deriving common fixed point results under a generalized Φ-contraction condition in symmetric spaces. Some examples are given to exhibit different types of situations where these conditions can be used and to distinguish our results from the known ones. As an application, an existence result for certain systems of integral equations is presented

Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces

[EN] New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.Abtahi, M.; Kadelburg, Z.; Radenovic, S. (2018). Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces. Applied General Topology. 19(2):189-201. doi:10.4995/agt.2018.7409SWORD189201192M. Abtahi, Fixed point theorems for Meir-Keeler type contractions in metric spaces, Fixed Point Theory 17, no. 2 (2016), 225-236.M. Abtahi, Z. Kadelburg and S. Radenovic, Fixed points of Ciric-Matkowski-type contractions in $nu$-generalized metric spaces, Rev. Real Acad. Cienc. Exac. Fis. Nat. Ser. A, Mat. 111, no. 1 (2017), 57-64.B. Alamri, T. Suzuki and L. A. Khan, Caristi's fixed point theorem and Subrahmanyam's fixed point theorem in $nu$-generalized metric spaces, J. Function Spaces, 2015, Art. ID 709391, 6 pp.V. Berinde and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory Appl. (2012) 2012:115. https://doi.org/10.1186/1687-1812-2012-115T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65, no. 7 (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31-37.Lj. B. Ciric, A new fixed-point theorem for contractive mappings, Publ. Inst. Math. (N.S) 30 (44) (1981), 25-27.Z. Kadelburg and S. Radenovic, On generalized metric spaces: A survey, TWMS J. Pure Appl. Math. 5 (2014), 3-13.Z. Kadelburg and S. Radenovic, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sciences 8:125 (2014). https://doi.org/10.1007/s40096-014-0125-6R. Kannan, Some results on fixed points-II, Amer. Math. Monthly 76 (1969), 405-408.W. A. Kirk and N. Shahzad, Generalized metrics and Caristi's theorem, Fixed Point Theory Appl. 2013:129 (2013). https://doi.org/10.1186/1687-1812-2013-129V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349. https://doi.org/10.1016/j.na.2008.09.020N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), 983-992. https://doi.org/10.1016/j.na.2010.09.055J. J. Nieto and R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, Engl. Ser. 23, no. 12 (2007), 2205-2212. https://doi.org/10.1007/s10114-005-0769-0P. D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. 64 (2006), 546-557. https://doi.org/10.1016/j.na.2005.04.044B. Samet, Discussion on 'A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces' by A. Branciari, Publ. Math. Debrecen 76 (2010), 493-494.B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517. https://doi.org/10.1016/j.na.2010.02.026I. R. Sarma, J. M. Rao and S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2 (2009), 180-182. https://doi.org/10.22436/jnsa.002.03.06T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098, 5 pp.T. Suzuki, B. Alamri and L. A. Khan, Some notes on fixed point theorems in v-generalized metric spaces, Bull. Kyushu Inst. Tech. Pure Appl. Math. 62 (2015), 15-23.M. Turinici, Functional contractions in local Branciari metric spaces, Romai J. 8 (2012),189-199

Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

In this paper, inspired by the idea of Meir–Keeler contractive mappings, we introduce Meir–Keeler expansive mappings, say MKE, in order to obtain Krasnosel’skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir–Keeler mapping and expansive Krasnosel’skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel’skii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7–8):3229–3239, 2009]

Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones

New fixed point results in b-rectangular metric spaces

In this work, the class of b-rectangular metric spaces is introduced, some fixed point results dealing with rational type contractions and almost generalized weakly contractive mappings are obtained. Certain examples are given to support the results