Zakiye Khalili - Department of Mathematics, University of Birjand, Birjand, P. O. Box ۴۱۴, ۹۷۱۷۸۵۱۳۶۷, Birjand, Iran.
Alireza Janfada - Department of Mathematics, University of Birjand, Birjand, P. O. Box ۴۱۴, ۹۷۱۷۸۵۱۳۶۷, Birjand, Iran.
Mohammad Reza Miri - Department of Mathematics, University of Birjand, Birjand, P. O. Box ۴۱۴, ۹۷۱۷۸۵۱۳۶۷, Birjand, Iran.
Mohsen Niazi - Department of Mathematics, University of Birjand, Birjand, P. O. Box ۴۱۴, ۹۷۱۷۸۵۱۳۶۷, Birjand, Iran.

This article introduces the notion of L_p-C^*-semi-inner product space, a generalization of the concept of C^*-semi-inner product space  introduced by Gamchi et al., where we consider H\"{o}lder's inequality instead of Cauchy Schwartz' inequality. We establish some basic results L_p-C^*-semi-inner product spaces, analogous to those valid for C^*-semi-inner product spaces and Hilbert C^*-modules.

Hilbert C^*-module, Semi-inner product, derivation, Anti-Derivation