Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points

We consider a lower bounded function on a complete metric space. For this function, we obtain conditions, including Caristi’s conditions, under which this function attains its infimum. These results are applied to the study of the existence of a coincidence point of two mappings acting from one metric space to another. We consider both single-valued and set-valued mappings one of which is a covering mapping and the other is Lipschitz continuous. Special attention is paid to the study of a degenerate case that includes, in particular, generalized contraction mappings.     

Author’s response to Dr. Wadee and Yiatros’ discussion of my paper: “On interactive buckling in a sandwich structure” (ZAMP, vol. 61, pp. 565–577, 2010)

In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565–577 2010) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors.     

Author’s response to Dr. Wadee and Yiatros’ discussion of my paper: “On interactive buckling in a sandwich structure” (ZAMP,vol. 61, pp. 565–577, 2010)

In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565–577 2010) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors.